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Uniqueness of homogeneous CAT(0) polygonal complexes

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Abstract

We provide a combinatorial condition on a finite connected graph, \(L\), for which there exists a unique CAT(0) polygonal complex such that the link at each vertex is \(L\). Under the further assumption that the polygons have an even number of sides we prove that this condition is also necessary, and that there are either one or a continuum of non-isomorphic such complexes.

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Acknowledgments

This research was motivated by the problems presented in the survey paper by Farb et al. [4]. I am grateful to my advisor Michah Sageev for introducing me to these questions and for his continuing encouragement and advice. I would also like to thank Anne Thomas for helpful conversations and comments on the manuscript, and an anonymous referee for careful reading and useful remarks.

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Authors and Affiliations

  1. Department of Mathematics, Technion—Israel Institute of Technology, 32000 , Haifa, Israel

    Nir Lazarovich

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  1. Nir Lazarovich
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Correspondence to Nir Lazarovich.

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Supported in part by The Adams Fellowship Fund.

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Lazarovich, N. Uniqueness of homogeneous CAT(0) polygonal complexes. Geom Dedicata 168, 397–414 (2014). https://doi.org/10.1007/s10711-013-9837-2

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  • DOI: https://doi.org/10.1007/s10711-013-9837-2

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