Thinking topologically about urban climate finance: geographical inequalities and Mexico’s urban landscapes of infrastructure investment

ABSTRACT Clearly, the resources available for tackling the deleterious effects of climate change differ starkly within and between cities. Increasing evidence indicates that uneven climate investments further aggravate these inequalities in cities’ capacities to combat climate change. This article delves further into the efforts of urban climate finance (UCF) initiatives – programs that seek to foster “green investment” – and the spatial relations they forge: How do these initiatives shape global geographies of (dis)investment in urban climate action? We suggest that a topological conceptualization provides an analytic for examining the spatial functioning of UCF initiatives. Considering how these initiatives intervene in Mexican cities, this relational conceptualization highlights how they forge relations marked by heightened intensity of climate action in some sites where the initiatives aim to pull resources together to bring climate projects about. Simultaneously, we show the disconnection of other urban sites to income streams, pushing cities further “off the map” of available support.


Introduction
The widening gulf between urban landscapes threatened by climate-related risks and those marked by relative climate security is one of the crucial political issues of our times.While the resources available for tackling the deleterious effects of climate change differ starkly within and between cities, an increasing body of evidence indicates that uneven climate investments further aggravate these inequalities in cities' capacities to combat climate change (Ponder, 2021;Rice et al., 2022).As these investments map onto historically rooted but ongoing relations of colonialism and racial capitalism, scholars maintain that they deepen what Boaventura de Sousa Santos (2007,2016) calls the "abyssal line": a profound sociospatial division based on these interlocking systems of oppression (Bledsoe & Wright, 2019;Bonilla, 2020a).However, the geographies emerging in the preparation for, or in the wake of, such investments have not yet been adequately explored.In this paper, we delve deeper into the spatial relations emerging through, and in anticipation of, global climate investment at the urban scale.We focus on an increasing number of global initiatives set up to facilitate urban climate finance (UCF): city-focused programs launched by city networks (such as C40 Cities), multilateral development banks (such as the Word Bank), and philanthropical institutions (such as the Rockefeller Foundation) in order to foster investment in urban adaptation and mitigation measures. 1,2How do these initiatives shape global geographies of (dis)investment in urban climate action?How do they unmap and redraw engrained landscapes of austerity, and neglect?
We suggest that a topological conceptualization of space can provide an analytic for examining the spatial functioning of UCF initiatives and the way they rearticulate extant urban geographies of inequality.Topological thinking has increasingly found its way into urban studies (Martin & Secor, 2014;Zhao, 2020) and geography (Allen, 2011(Allen, , 2016) ) to foster relational thinking about topics such as the spatial relations of finance (Harker, 2017;Langley, 2020) and climate change (Goldman et al., 2016).The literature in these fields has employed topologies to describe transformations of spatial shapesthrough twisting, folding, or reaching across metric spacewhile maintaining the structural relations of space (Allen, 2011, p. 285).Reading the spatial functioning of UCF initiatives through a topological lens pinpoints two main levels of analysis.First, of the practices through which these initiatives reconfigure urban spatial relations while encouraging climate investment; for instance, by establishing connections that "dissolve" metric space when actors make their presence felt in urban policy from afar (and thus relationally bridge space); or by disrupting relations, when the efforts to build and maintain connectivity break apart, with potential consequences for cities' income streams.Second, a topological reading offers a more nuanced understanding of the emerging topological spaces (Lury et al., 2012).This includes considering they ways in which these spaces are entangled in and shape extant territorial divisions and inequalities; for instance, when the spatial relations described map onto urban landscapes long shaped by redlining and austerity governance.
To understand the topological practices and emerging topological spaces by which UCF initiatives operate, our analysis draws on research on the ways in which these initiatives engage in and negotiate with secondary cities to prepare the foundations for green investment, which is frequently focused on infrastructure.Alongside the analysis of their global operations, this paper centers on how UCF initiatives seek to foster investment in secondary cities in Mexico, in order to capture the topological practices that emerge from two characteristic ways in which they function.First, we explore how the initiatives' financial approachesincluding project pipelines and blending schemesextend the reach of development practitioners, technical experts, and Wall Street elites.Second, we identify topological practices that intensify these relations; for instance, when practitioners cluster around a limited number of locations, rendering these sites exclusive spaces with exceptional access to resources and expertise.Finally, we deduce absences from the initiatives' intense presence in these sites and discuss the fragility of the relations we have previously described; for instance, when cities are cut off from global funding streams.In distinction to a (multi)scalar frame of analysis or territorial approaches to understanding the spaces of urban (dis)investment and climate risk, a topological lens points to the ways in which UCF transcends the hierarchical workings of institutional levels or the binaries of North and South.Together, what emerges is a geography of relational absences and presences marked by a heightened intensity of climate action in some cities where UCF initiatives pull resources together to bring about a limited selection of projects.At the same time, we are witnessing increasing difficulties among other cities to access support, pushing cities "off the map" (Robinson, 2002) of available funding for mitigation and resilience measures.
We continue by providing an overview of the literature situated at the intersections of urban, financial, and development geography that explores the uneven geographies of UCF.In the subsequent Section, we operationalize topological perspectives as an analytic for reading the making of these geographies.Following on, we provide an empirical discussion of the topological practices of UCF initiatives and their interventions in Mexican cities, before concluding on the geographies that emerge from this.

Situating global climate finance
Over the past decade, a growing body of scholarship has emerged at the intersections of research on urban climate governance and the financialization of urban climate and nature.In particular, we build on work that paints a nuanced picture of the deepening spatial divisions and uneven processes of development that emerge in the context of climate investment and climate change.After further contextualizing UCF within this scholarly field of inquiry, we review the spatial imaginaries prevalent within it.

The urbanization of UCF
Climate finance has been urbanized.Since the 2015 adoption of the SDGs, cities have widely been marked as the sites from which to solve the climate crisis.A bourgeoning body of literature has described accompanying shifts in the governance of urban climate action.Alongside the involvement of transnational municipal networks in climate action (TMNs) 3 (Bulkeley & Betsill, 2006;Kern & Bulkeley, 2009), research in the field has shed light on the increasing power of non-state actorse.g.consultants, finance experts, private regulators, institutional investors, development cooperations, multilateral banks, and philanthropic institutionsin these polycentric arrangements (Bracking & Leffel, 2021;Graham, 2017;Leitner et al., 2018).
This work not only notes how these networks unite a wide variety of actors in shared frames (Toly, 2008), it also highlights the convergence of their aims (Grubbauer & Hilbrandt, 2020;Long, 2021).For instance, dominant donors have moved away from traditional funding through aid towards a framing of development through private investment (Carroll & Jarvis, 2014;Mawdsley, 2018a).The alignment of these diverse interests (e.g.those of development banks with private finance and philanthropic institutions) has facilitated the development of powerful partnerships among these groups.
Alongside this, scholars have argued that particularly since the 2007/08 economic crisis, financial considerations have become crucial in shaping the implementation of climate measures and have embedded the logic of economic expansion in the production of urban climate solutions (Grubbauer & Hilbrandt, forthcoming;Knuth, 2018;Ouma et al., 2018;Taylor & Weinkle, 2020).Because these solutions offer new modes of financialization, investment, and profit-making, urban research has found that municipal climate action has frequently been framed around market-based interventions that promote profitability considerations, market discipline, and experimentation with new financial mechanisms and processes of "market-making" (Bracking & Leffel, 2021;Long, 2021).Vanessa Castán Broto and Enora Robin consequently stress that such "climate urbanism" serves the "securitization of cities (…) to maintain the reproduction of capitalist economies" (2021, p. 716).The framing of UCF as a central solution to climate change is exemplary for their claim.
When considering the planned material changes in cities, scholars have found that UCF's material interventions center on large-scale infrastructure projects that facilitate green growth (Silver, 2017;Schindler & Kanai, 2021), frequently through smart urban solutions (Rebentisch et al., 2020).UCF initiatives have discursively linked project investments to set climate goals through the so-called "infrastructure investment gap" (OECD, 2017, p. 92).This gap frames urban adaptation and mitigation measures with reference to a calculation of cities' assumed financial needs for project investment. 4As projects are easier to sell and financialize than more fragmented planning interventions, this framing also facilitates profit-driven financial investment.Moreover, research has found that it has been easier to align the aforementioned polycentric structures around one common goal or project (Grafe & Hilbrandt, 2019).The UCF initiatives that are at the core of this paper emerge in the context of these changing practices of governance and finance and associated shifts in cities' strategies to achieve material transformations.

How UCF initiatives shape urban geographies of inequality
If we inquire, then, into how UCF initiatives further the differentiation of geographical space through, and in anticipation of, global climate investment at the urban scale, the literature paints a varied picture of these spatialities.In seeking to understand these geographies, we are particularly inspired by scholars who address how UCF is embedded in the structural violence of racio-colonial governance (Bonilla, 2020a, p. 2).This body of work has been able to show that the implementation of climate urbanism echoes existing modes of coloniality and racial capitalism, as well as how these dynamics dovetail with geographies of (climate-related) inequalities (Bigger & Millington, 2020;Bonilla, 2020b;Ranganathan & Bratman, 2021;Robin et al., 2020).While the geographies this work discusses are far from clear, four spatial imaginaries stand out: First, scholars highlight how the geopolitics of development assistance and related green investment strategies revive and deepen longstanding North-South divisions (Kalaidjian & Robinson, 2022;Mawdsley, 2018b;Schmitt, 2020;Webber et al., 2021).For instance, David Ciplet et al. employ World-systems theory to consider how climate finance reproduces uneven relations of power and dependency between "core and periphery".While the authors suggest that where finance flows is predominantly driven by financial interest, they also give nuance to this claim by pointing out that climate vulnerability or the interests of peripheral states likewise influence such allocations (Ciplet et al., 2022, p. 9).Others have argued that the dominant modalities of development assistance reinforce relations of dependency and divisions between debtor and lending countries (Perry, 2021).As such, contemporary processes of "accumulation by dispossession" (Harvey, 2003) overlay a landscape marked by the infrastructural deficits produced by past regimes; for instance, longstanding Washington Consensus reforms and subsequent liberalization agreements through which development banks undermined the construction of urban infrastructure necessary for adaptation and mitigation (Gonzalez, 2020, p. 118).Moreover, they revive colonial epistemologies, as their taxonomies of investment are written in the North before being transferred to the South (see for instance Ouma, 2010).In this way, UCF is imagined to move what Boaventura de Sousa Santos calls the "abyssal line" (de Sousa Santos, 2016), a line that excludes populations through the production of multiple forms of difference, marking them as inferior and rendering them invisible.Similarly, Joshua Long et al. (2020, p. 39) speak of a growing climate apartheida "global apartheid [that is] exacerbated by the climate crisis" (see also Rice et al., 2022), pointing to a spatial formation of separation and segregation.
Second, the literature pictures a continualbut contestedspatial expansion of investment efforts, with the aim of integrating ever more cities into globally expanding networks of climate finance.Consider, for instance, how development agencies and associated green governance actors have become involved in securing private capital in order to incentivize and scale up green investments.Looking at San José, Costa Rica, Andres Jiménez Corrales and Pablo Zagt Hernandez ( 2022) have pointed to the policies through which the Inter-American Development Bank (IDB) enrolls (ever more) Latin American cities in narratives of sustainability that seek to create conditions for (green) investment.Monika Grubbauer and Hanna Hilbrandt (Grubbauer & Hilbrandt, forthcoming;Hilbrandt & Grubbauer, 2020) have pointed to the hurdles that efforts to expand climate finance to the South face in practice.Others point to ways to overcome these challenges and move the market "Southward".Daniela Gabor calls this the "'development as de-risking' paradigm" (Gabor, 2021, p. 429), to describe the way development serves to "'escort' global (North) institutional investors and the managers of their trillions into development asset classes" (Gabor, 2021).Together, this literature depicts ongoing but contested attempts to move private climate finance into peripheral, or frontier regions in the South.
Third, scholars argue that while the financialization of nature maps onto geographies shaped by colonial relations, what emerges is not a linear division between a presumed territorial North and South, but the formation of "zone(s) of extraction" (Perry, 2021, p. 364) for the appropriation of profits and ecosystem services.For instance, scholarly work on financializing nature (Bracking, 2019) through carbon trading and other nature-based financial mechanisms has pointed to the spatial effects of experimenting with and consequentially exploiting Southern natures.The rise of a variety of mechanisms for "banking nature" (Sullivan, 2013) that build on ecosystem services to gain financial yield by trading in carbon offsets provides a useful example. 5For Perry, these mechanisms are driven by a "colonial-climate ontology" (2021, p. 364), which casts the South as exploitable and expandable, marked by zones for resource extraction and sacrifice; or as Adam Bledsoe and Willie Wright put it, as an empty "no man's land" that is "open to occupation, and subject to surveillance and assault" (2019, p. 11).What emerges in this work is a geographical imagination in which uneven development manifests spatially in delimited and selective interventions and residual spaces of abandonment.
Finally, scholars describe how climate investments further intra-and inter-urban inequalities (Bigger & Millington, 2020).Analyzing the municipal indebtedness of Jackson (Mississippi) and other majority-Black cities, Sage Ponder (2021) documents how the issuance of green bonds reproduces the financial subordination of these cities, which have historically paid more for their debt than majority-White towns.Moreover, geographers focusing on the scale of the neighborhood describe how climate urbanism shapes processes of urban exclusion.For instance, as Patrick Bigger and Nate Milington's comparison of green bond investments in New York and Cape Town shows, the infrastructural politics through which indigent communities bear the risks of this investment deepen patterns of racialized (and often classed) austerity (Bigger & Millington, 2020).As Sara Safransky notes, green financial mechanisms of risk evaluation revive redlining practices through new technological tools (2020), by means of what she terms "algorithmic violence."Through this phenomenon, financial flows are blocked from particular areas and perpetuate their infrastructural deprivation, and neglect.Similarly, an expansive body of literature has illustrated how green gentrification (Anguelovski et al., 2017) expands what Roy (2019) calls "the racial banishment of minority populations".Together, this literature documents increasing divisions between cities and neighborhoods with(out) access to funding streams and the accompanying processes of in/exclusion that these divisions generate for their populations.
These fields of literature describe the geographies emerging through the entanglement of cities' climate efforts and global attempts to support the financialization of these efforts through multiple and interlocking spatial patterns: the deepening of the North-South divide, the Southward expansion of geographical investment spheres, the formation and expansion of Southern extraction zones, and the strengthening of inter and intraurban divisions.Often these spatial accounts are focused on local individual case studies that analyze the spatialities of UCF incidentally or at a particular scale.In sum, the debate lacks a more systematic analysis of the spatial functioning of UCF and an analytical vocabulary that is well equipped to capture the associated geographical shifts.

The topologies of UCF: an analytical framework
We suggest that a topological analysis is able to plot the spatial functioning of UCF.Originally a field of mathematics, topological analysis centers on the study of geometrical properties that remain unaffected by the continuous deformation of their shape or size; or, as Allen puts it, on how "things retain their integrity despite being twisted or stretched out of shape" (Allen, 2011, p. 285).In the last two decades, topologies emerged as a register of geographical analysis (Allen & Cochrane, 2010;Enright, 2017;Faulconbridge, 2013;Gregory, 2003) to grasp the quality or intensity of relations and their endurance under conditions of transformation (Martin & Secor, 2014, p. 47).They are deployed, amongst others, to gain an understanding of phenomena such as the spatialities of finance (Allen & Pryke, 2013;Langley, 2020), the consequences of climate change (Goldman et al., 2016), and the everyday experience of urban space (Harker, 2014;Secor, 2013).Allen explains this emergence through the increasing failure of flat, territorial understandings of space to capture the spatial experiences of a globalized world in which technological developments make it easy to overcome vast geographical distances (Allen, 2011, p. 283). 6Transcending the stacked, vertical imageries of scalar accounts or the horizontal ones of extensive space envisioned in spatial analyses centered on mobilities and networks (Allen & Cochrane, 2010, pp. 1072-1073) is particularly crucial when it comes to understanding the geographies of UCF, as they workwe argueto establish connections across metric distance and scale.
In line with relational approaches to space (Allen, 2003), topological analysis takes space to emerge through practice (Allen, 2016, p. 6); that is, practices make up the spaces in which they take place.This implies an understanding of space in which geographies are actively producedenacted, maintained, and stabilizedrather than given (Allen, 2011, p. 286).Topological space is produced through a particular set of spatial practices that forge connections (Allen, 2011, p. 292) in ways that cut out or close "the gap between near and far" (Allen, 2011, p. 293).Unlike in a networked imaginary of space, in a topological understanding, these practices are "dissolving, not traversing" metric space (Allen, 2011, p. 290).Thus, territorial space is, to cite Allen once more, "bridged relationally" (Allen, 2011, p. 289) when topological practices stretch, diminish, or erase a space of metric distance (Allen, 2011, p. 294) as they "hook up" agents (Allen, 2011, p. 288).Allen understands these practices to be power-laden: they allow authority to be exercised across spatial divides, with actors making their presence felt in other places; or they produce absences despite spatial proximity, by inflecting, separating, and twisting space.
Paul Langley provides an illustrative example when he refers to the far-reaching powers of corporate social finance that traverse territories to "anchor" (Langley, 2020, p. 131) market instruments in social policy programs as a topological effort.Rather than viewing "the marketization of social finance" (Langley, 2020, p. 132) as an outward extensiona roll-out crossing territories and borders into new "frontier regions" -, Langley describes it as folding impact standards into new arenas of social and political life.As these practices reach across and transcend distance without their effect diminishing across metric space, metric space and scale lose relevance and dimension.As his research shows, topological practices work through presence rather than distance or proximity, and reach rather than metric extension or expansion.
Topological space emerges through these practices as a temporarily stabilized arrangement that is entangled in topographical space.Christopher Harker, for instance, uses a topological lens to capture the non-metric, relational space-time of debt through its active production and performance in everyday life in Palestine (Harker, 2017, p. 608).Crucially, for Harker, reading space through a topological perspective does not imply omitting other spatial relations from the analysis.Rather, reading topologies alongside a topographical frame pinpoints how different spatial relations co-constitute space, operating in a productive (theoretical) tension with one another.As Harker argues, both are generative of one another: They combine in ways that can only be read in understanding the conjuncture of the two (see also Langley, 2020, p. 140), for instance, when topological relations of debt that reach across distance map onto a landscape marked by colonial-territorial relations (Gregory, 2003).
In this paper, a topological framework opens up a spatial analytic to describe how the practices of UCF initiatives and urban practitioners transcend and interact with the "fixed distances" and "well defined proximities" (Allen, 2016, p. 2) of the territorial divisions and inequalities of climate vulnerability, economic precarity, and the engrained legacies of racial exclusion and coloniality.We posit that this production of space is best captured through a twofold frame of analysis.First, we mobilize an analysis of topological practices through which places are incorporated into the functioning of UCF and ask how actors overcome territorial distances and intensify or generate new relations to establish presence across metric space.How, for instance, are sites placed within or beyond the reach of financial investment and development aid when UCF initiatives become present in municipalities, connect with local practitioners, and broker deals with them; or when new ratings cut cities off from access to financial networks?Crucially, looking at the ways in which these practices establish space allows us to understand geographies as socially produced, and to see how this production is sometimes difficult, fragile, and contested.Second, we argue that a topological analysis offers a more nuanced understanding of the topological spaces emerging in the wake of UCF initiatives' efforts.It enables us to pinpoint the changing qualities of spatial relations when UCF initiatives intensify social interactions, governance relations, or financial exchanges with selected sites, thereby bridging scales and metric distance, or twisting and folding space, to use a topological vocabulary.This also implies an understanding of where connections break apart (i.e.how topological practices cut off some places), thereby (re)producing cycles of neglect and the absence of resources and relevant knowledge.As noted above, it is crucial to understand these practices and spaces in the interaction of topological and topographical space (Paasi, 2011;Paasi & Zimmerbauer, 2016).

Tracing the topologies of UCF
Before we delve into the topological practices of UCF initiatives and the geographies of inequality that emerge from them, we introduce the methodological basis for this empirical discussion, including the context through which we think.This paper builds on data collected in 2021 and 2022 in the course of a research project that investigates the production of climate urbanism through a set of UCF initiatives.While driven by a range of partner institutions (including philanthropic bodies, such as the Rockefeller Foundation, multilateral banks, such as the World Bank, and city networks, such as ICLEI -Local Governments for Sustainability), these initiatives center on similar strategies and aims: on so-called project preparation facilities that foster the preparation of bankable infrastructure projects, as well as on capacity-building efforts that seek to provide technical assistance to support the implementation of these preparations on the ground.Nick Bernards calls both processes "anticipatory marketization," which he describes as "preparing the institutional and infrastructural substrates for market exchange in hopes that buyers and sellers will turn up" (2022, p. 2).In this project, we aim to understand how UCF initiatives work to shape urban policy and infrastructural development; as well as how they were sought after or received on the ground, that is, how urban policy-makers and government agencies "arrived at" territorialized urban solutions (Robinson, 2015).
This paper considers the functioning of a set of global UCF initiatives alongside an analysis of their workings in Mexican cities.While we selected this context as the country is frequently classified an "emerging market," making it attractive to possible infrastructure investment, our research on UCF initiatives that operate on the global stage suggests that similar topological practices are at play in other national contexts.We focus particularly on mid-sized or secondary cities.Long overlooked in funding programs and policy that has focused attention on capital cities, these cities are now targeted by UCF initiatives to forge the necessary relations, infrastructure, and structural changes needed to respond to their predicted growth.In particular, the paper builds on a content analysis of the reports of the UCF initiatives in focus, policy programs, blogs, and feasibility studies (Kuckartz, 2019).We selected these initiatives on the basis of the CCFLA (2017) mapping report that lists about 90 UCF initiatives.Additionally, we use data from 30 interviews with the managers of transnational municipal networks, multilateral and regional banks, local technical consultants, government advisors, as well as planners and city officials, which lasted approximately one hour and were conducted mostly via zoom during the COVID-19 pandemic.
Let us also introduce the current politico-economic context of Mexican climate and economic policy, in particular in relation to the country's secondary cities.Since 2018, Mexico's investment landscape has been marked by Andrés Manuel López Obrador's term in government and his proclamation of the Cuarta Transformación [Fourth Transformation]a project of state transformation with the aim of combatting insecurity, corruption, violence, and socioeconomic exclusion.In practice, however, the climate policies of this regime can be situated in the context of Latin American neo-extractivism.For instance, López Obrador's focus on strengthening brown industriesin particular the state's oil company PEMEXhas crucial consequences for the environment and local communities (Svampa, 2019).Similarly, the Tren Maya [Mayan Train], a flagship infrastructure project that extends the country's railway system in the southwest, is exemplary for how the Cuarta Transformación is violating the human rights of Indigenous communities while creating ecoterritorial conflict (Casañas, 2021).
While scholarship on the financialization of infrastructure in Mexico in general and through development finance in particular remains scarce (see, however, Reis, 2017, or Jiménez Corrales & Zagt Hernandez, 2022, for work on San José, Costa Rica), a growing body of literature on the financialization of housing (Gasca Zamora & Castro Martínez, 2021;Heeg et al., 2020;Janoschka & Salinas Arreortua, 2017;Reyes & Basile, 2022), as well as literature that speaks more directly to the financial policies of the current political regime (Hanrahan & Aroch Fugellie, 2019;Reis, 2020) paints the picture of an increasingly uncertain investment space.While Obrador labels the Cuarta Transformación itself "anti-neoliberalism", the very investment relations this discourse seeks to supplant continue to characterize the governance and financial conditions of Mexican cities (interviews, 03.02.2022; 01.02.2022)although, as we will show, perhaps in more fragile, ambiguous, and covert ways.Alongside these political uncertainties, pandemic-related austerity measures have made it challenging for smaller cities that have historically been underfunded to finance climate projects.
In this context, UCF initiatives appear particularly promising when it comes to financing much needed infrastructure.Frequently understood according to multi-level governance frameworks (Bulkeley & Betsill, 2013) that stress the influence of cities as global political actors (Oosterlynck et al., 2019) or the leverage of global actors at the local scale, here we argue that the governance of UCF initiatives engenders a topological space.Our analysis centers on topological practices that emerge from key characteristics of UCF initiatives.First, we sketch out how the particular financial frameworks they promote work through practices of reach, thereby shaping geographies of risk and related infrastructure investments.Second, we highlight a set of topological practices that intensify connectivity and emerge from the organizational architecture of the initiatives and the ways in which they anchor their efforts in space.Third, we discuss the fragility of the relations that are built, their rupture, and the production of relational absences.These are certainly not the only ways in which UCF initiatives act topologically, but they are relevant to understanding the spatial shifts we seek to highlight.

Extending reach
As previously noted, UCF initiatives such as the WRI's CityFixLabs or the Climate-KIC's Low Carbon City Lab are broadly united around the aim to "crowd in" finance in places not previously "serviced" by finance or (increasingly) considered too risky for investment, to use the terminology of the UCF community.While differing slightly in their methodologies, they center on the preparation of project pipelines that include the "matchmaking" between cities and possible investors.Considering how their specific financial schemes relationally bridge the gap between local infrastructure needs and a global "wall of money" (Fernandez & Aalbers, 2016) indicates the topological workings of these initiatives.To understand how these practices rearticulate the geographies of climate investment, we consider how they employ practices of extended reach that overcome territorial space to bind distant cities into circuits of infrastructure investment.
The Transformative Action Program (TAP) supported by ICLEI, the Global Fund for Cities Development (FMDV), and GIZ's Felicity initiative, provides a prime example of how UCF initiatives build connection through topological practices of reach. 7The TAP supports cities in making projects bankable to build a new "green" asset class from which investors can harvest revenue streams.To enter the TAP pipeline, tools such as Global Infrastructure Basel's (GIB) "smart scan tool" allow cities to self-evaluate their projects.Cities can subsequently apply, go through a screening process, and once a decision is made to carry their projects forward, the initiative offers services to improve the project planning through intensive technical support (interview, 31.01.2022).To enter into the TAP database, there is "a lot of back and forth" (interview, 31.01.2022).As we were told, this "back and forth" often includes the completion of a feasibility study, in which external experts collect data for cities that lack the capacities to analyze aspects such as the cost of a particular project.Crucially for an understanding of the topological spaces that UCF generates, being included in the TAP pipeline standardises projects through the evaluation of their financial architecture and sustainability (ICLEI, 2021).Related practices of ranking, rating, calculating, and listing create transparency and prepare investability, as they make projects legible independent of their local or national context.Standardizing infrastructure projects in this way works to integrate these sites into an investment realm, thus investors to reach across metric space.
In a similar way, processes of blendingthe de-risking of private capital investment through philanthropic, development, or state funds (see OECD, 2015)bridge distance, fold metric space, and extend the reach of finance to lift cities' investment projects across an imaginary line that marks cities as too risky for investments (or as becoming risky through increasing climate hazards).In a topological reading, these blending mechanisms twist the map-based geographies of risk (Koslov, 2019) to integrate spaces into a realm of investability, while omitting those of heightened climate vulnerability or financial risks from view.The financial architecture of a project we studied in the municipality of Naucalpanto develop the city's landfill into a solid-waste treatment plantis exemplary in this regard.Planned through a public-private partnership, the financial architecture of this waste-to-energy scheme employs practices of reach: To ensure stable income for investors from energy sales and guarantee the project's profitability the solid-waste treatment plant is planned to be funded through a credit from the Fondo Nacional de Infrastructure (FONADIN), thereby hedging risks through state funds (interview, 03.02.2022).Additionally, "ring-fencing" (Allen & Pryke, 2013) its financial operations through a Special Purpose Vehicle allows the project to avoid being embedded in the local context, enabling a "rate of return that can be accessed from afar" (Allen & Pryke, 2013, p. 1327).Ultimately, this financial architecture also shapes the urban landscape as it establishes a geographical pattern in which projects are shielded as islands of investment from other city space.
Together, the TAP pipeline and the Naucalpan project indicate how UCF initiatives employ topological practices of reach to drive geographies of inequality.Thereby project standards and blending schemes bind projects in circuits of investment, not by means of extension but by reaching across and dissolving metric space.

Intensifying relations
In order to highlight the spatial functioning of UCF initiatives and render legible how they rearticulate extant geographies of inequality, it is also useful to consider how their topological practices intensify sociospatial relations.Particularly, as we seek to illustrate, UCF initiatives tightly connect a limited number of cities with global finance in intense relations of presence, while concentrating these efforts on a narrow selection of climate projects.
Despite many of the initiatives' constant efforts to look for new partners and widen investment possibilities, a topological perspective highlights how the ways in which they operate work to pool resources in uneven ways.As a city administrator in a local municipal department told us, once they had become part of one initiative, they became integrated into an increasing number of them: "It's like a cascade," she noted (interview, 21.01.2022).Their participation in one initiative provided them with a track record, signaling local financial expertise and a willingness to financialize their infrastructure.Similarly, the director of a planning institute in another city noted: "Probably five or six years ago, we only had one friend and now we have ten.(…) We are getting more and more credibility on the international level" (interview, 07.01.2022).While UCF initiatives push some Mexican "donor darlings" (interview, 06.09.2021) to the fore, our interviewees maintained that through the same "cascade logics," most technical assistance would divert to cities in Colombia, where our respondents considered the national context currently more amenable to financializing urban infrastructure.In the Mexican context of austerity and centralized government politics, secondary cities in particular (either because of this political environment or because they are unable or unwilling to play by the rules of UCF) are faced with increasingly limited financial resources (interview, 01.02.2022).
The waste-to-energy project we studied in the municipality of Naucalpan exemplifies these intensified relations of presence in that space.Throughout the processes of designing this project and its financial architecture, more than five UCF initiatives got involved to deliver feasibility studies, educate local practitioners, and convince municipal politicians of the project's relevance; in short: to bring the project about. 8As has previously been outlined by a significant body of research on the influence of globally circulating policy ideas (e.g.Peck & Theodore, 2015), we witnessed the presence of these initiatives and their "footloose" experts and external advisors, who were (relationally) connected yet working at a (metric) distance across different initiatives (interview, 25.08.2021).These communities of practice come together in workshops, webinars, and expert fora across the presumed North and South hemispheres, cohering around a set of perspectives and opinions that are frequently focused on "neoliberal ecopolitical principles" (Toly, 2008, p. 350).As a result of this alignment and intensified connectivity, in our interviews, we encountered similar graphics depicting this development scheme in multiple presentations related to various projectsthe same pillars leading to the implementation of this PPP-funded waste-to-energy scheme embedded in local implementation guidelines.The promotion of these ideas and our travels on Zoom were presencing the graphic in multiple spaces in topological ways.
The tight entanglements of these initiatives and the alignment of their strategies enable them to concentrate efforts on one location or on a limited range of projects.By establishing these focal points of attention which also connect various concerned actors, they shift urban geographies not by means of metric extension (i.e. by rolling out funding across space) but by intensifying relations with certain locations while producing relational absences in the spaces they reach across.

Fragility and rupture
Let us then consider the omission of certain sites in the initiatives' engagement, as well as the fragility of the topological efforts we described, creating the geographical absences we also seek to analyze.Most crucially, UCF initiatives engage topologically by sorting project ideas and their further investment according to standards of bankability or creditworthiness (interview, 03.09.2021).The fact that only those projects deemed to be bankable receive funding means that decentralized solutions, for instance, which are unlikely to be able to be ringfenced, are excluded from funding, putting weight on infrastructure solutions that often lack integration into broader city-planning.In this context, it is the projects that are particularly crucial to combatting the risks of climate change (adaption rather than mitigation projects) that rarely receive funding.As one of our interviewees told us: "It's very difficult to get support for adaptation projects.(…) Everybody is super loud about [the imperative] that adaptation projects [should be] supported more.But no one really has one" (interview, 03.09.21).That project finance is prioritized also means that vernacular, redistributive, decentralized, or community-based finance solutions are frequently omitted from view (Robin, 2022), making these solutions ever more difficult to realize.Crucially, these mechanisms may mean that fewer resources are left for integrative projects or the day-to-day necessities of disenfranchised local communities.Given their historical under-funding, smaller municipalities in particular find themselves with few other possibilities for financing infrastructure investmentmaking project schemes seem like good options even for actors concerned with questions of redistributive justice (interview, 07.01.22).
These discussions have demonstrated that UCF efforts are also emerging from the offices of municipal agencies, and the local politico-economic conditions of the participating cities, where, as Ludovic Halbert and Hortense Rouanet note, "resources from multiple horizons are pulled together in a given (…) development, from a fixed plot of land to capital allocated in distant investment committee boardrooms" (2014, p. 472).Local responsesthe pulling together of resourcesrely on the ability of urban actors to apply for such support, thus on local expertise, including the support of universities and planning institutions (interview, 21.01.2022).Consequently, the historical underdevelopment of such infrastructure or the lack of related expertise lowers the chances of municipalities to gain support, and exacerbates intermunicipal inequality, so that marginalized communities who already bear a disproportionate share of climate risks are doubly disenfranchised by the overlay of these territorial relations and the topographical practices we describe (Gonzalez, 2020;Zárate-Toledo et al., 2019).
Alongside these omissions, we noted the fragility of the relations that are built through the initiatives' engagement.In some instances, projects are excluded from pipelines or cities from access to further technical expertise when attempts to financialize peripheral economies are frustrated by policy changes (see also Bernards, 2022).For instance, the CityFixLab has documented huge dropout rates where the local political "buy-in" is not secured or maintained (interview, 31.01.2021).As national institutions play a key role in shaping cities' participation in UCF initiatives, Mexico's proclaimed regime of anti-neoliberalism frequently limits the success of these efforts to bring such a project about.The Naucalpan project was, as we were told, "as rare as hen's teeth" (interview, 03.02.2022).Still, at the time of writing, the implementation of this waste-to-energy scheme was on a knife-edge, as a change in the national energy law almost brought this project to a halt (interview, 03.02.2022, see also Cullell, 2022).Moreover, to prevent the project from being dropped by a new administration, project managers sought to institutionalize their progress in contracts and MOUs to make sure they would outlive multiple administrations.Being anchored through the buy-in of UCF initiatives would make it difficult, they reasoned, to get rid of the landfill scheme (interview, 07.01.2022).Still, the geographies emerging from these practices remain fragile, contested, and frequently difficult to realize.

Conclusion
This paper has argued that a topological conceptualization of space can provide an analytic able to render legible the spatial functioning of UCF initiativesthat is, how they reach across space and intensify relations to a limited selection of sitesand how they rearticulate uneven urban geographies, even if these relations frequently remain fragile and difficult to maintain.Looking at a set of financial practicesranging from project preparation measures to blending effortsprovided an understanding of how these initiatives aimed to overcome distance to relocate the borders of risk and investment through practices that extend the reach of development practitioners, technical experts, and Wall Street elites.In addition, we highlighted how UCF initiatives forge relations of intensive connectivity and establish presence, as they draw selected cities into an exclusive investment space.In this way, UCF initiatives aim to integrate some spaces deemed amenable to profit making into circuits of climate investments.
We deduced related absences.While the resulting adaptation and mitigation efforts work to extend reach and pull some cities deeper into the investment community, we noted how cities are omitted from global climate efforts when they fail to build or sustain such connections and find themselves without effective resources for necessary adaptation and mitigation efforts, particularly in urban landscapes in Mexico subject to heightened austerity and climate risks.These topological practices can separate physically proximate cities in terms of their access to resources, support, and ideas.Together, what emerges is a geography of relational absences and presences marked by a heightened intensity of climate action in a select group of cities where UCF pulls resources together to deliver urban projects.At the same time, the dominant discourse on UCF and the heightened intensity of activities in some realms obscure the vast inactivity in a "world of many Souths" (Roy et al., 2020).
However, we also argued that the relations that emerge through the efforts of UCF initiatives remain fragile.Building these relations can be frustrated by political uncertainties and the difficulties of finding bankable projects and of making cities creditworthy.While this is particularly true in Mexican cities, where discourses of anti-neoliberalism and unpredictable policy changes make investments risky, our interviews with globally active UCF initiatives confirmed existing research (Hilbrandt & Grubbauer, 2020;Nciri & Levenda, 2020) that highlights the failures to establish relationalities in other contexts as well.Available data remains scarce and inconclusive regarding the effective changes made at the municipal scale, particularly in secondary cities where global climate investment is not yet the norm.While a bourgeoning body of work highlights the discourse and policies of UCF (Long, 2021), the urgency of the climate crisis and the related force with which current climate action is driving the described geographical shifts call for more empirical research into the sociomaterial geographies of UCF: into the local consequences of such investment on the ground.In particular, we know little about the underlying legal and regulatory changesprocesses of structural adjustments targeting the urban contextfostered to facilitate and fortify existing efforts to bring green infrastructure investments about.
Beyond these empirical contributions, we aimed to engender further debate about a spatial conceptualization of UCF.As we argued, a topological approach contributes a more nuanced vocabulary to understanding the spatial practices and emerging geographies of UCF, one that is able to think alongside network and policy mobility approaches and scalar accounts.Such thinking can help us to avoid approaching North-South relations as binary territorial divisions.While it is easy to think that what de Sousa Santos calls "the abyssal line" demarcates a North-South division, practices of reach demonstrate that this line marks a non-territorial Souththat develops in the shadow of postcolonial and racial geographies, as Ananya Roy (2019) has pointed out.Moreover, a topological analytic can assist us in reading "the frontier region of marketization" (Ouma et al., 2013) beyond a spatial imagination of extension or the roll-out and rollback of finance by considering the quality and intensity of relations.And it can aid us in exploring the scaling of risk (Christophers et al., 2020 ) in a relational, conjunctural (Hart, 2018) way.As topological practices are always embedded in and produce relations of power, such an approach also supports an analysis of the modalities of power through which actual geographies are practiced.
To conclude, we suggest that shining a spotlight on the mechanisms that produce the geographies of inequality described here can work against the normalization and dominance of UCF initiatives and their claim to foster sustainable climate action.Clearly, a spatial politics able to redress the practices we have described needs to link its efforts to broader anti-racist and anti-colonial struggles (Ranganathan & Bratman, 2021).
Rather than saving the places where profitable investment can still be made, what is needed is a notion of reparative climate justice (Webber et al., 2022), which fosters infrastructures of redistribution, in order to move resources across the abyssal line.

Notes
1. Climate finance is commonly understood as "local, national or transnational financingdrawn from public, private and alternative sources of financingthat seeks to support mitigation and adaptation actions that will address climate change" (UNFCCC, 2021).2. The Cities Climate Finance Leadership Alliance's mapping report (CCFLA, 2017) provides a useful overview over these initiatives.3. See, for example, the Global Covenant of Mayors for Climate and Energy, ICLEI -Local Governments for Sustainability, C40 Cities Climate Leadership Group, or the UCLG -United Cities and Local Governments.4. The OECD estimates that to sustain growth US$95 trillion of investment in infrastructures (energy, transport, water and telecommunications) will be necessary between 2016 and 2030. 5.For instance, through UN clean development mechanisms (https://cdm.unfccc.int/).6.In understanding these relations, as Anna Secor rightly notes, relational geographers have been "topologists" for some time (2013, p. 433).7. See https://tap-potential.org/.See also the WRI's CityFixLabs funded by the Citi Foundation (http://thecityfixlabsmexico.org/).8. Including the involvement of the European Investment Bank; the Deutsche Gesellschaft für Internationale Zusammenarbeit (GIZ); Mexico-UK PACT; the private consultancy firm IDOM; the German development bank KfW; the Global Methane Initiative; the Climate and Clean Air Coalition; and the United States Environmental Protection Agency EPA.