Abstract
In this chapter, we state and prove Stokes’ formula. We first discuss the notion of a boundary or a corner of an orbifold and of a Kuranishi structure in more detail. The discussion below is a detailed version of [FOOO4, the last paragraph of page 762]. See also [Jo1, page 11]. [Jo3] gives a systematic account on this issue.
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Notes
- 1.
This is a standard definition going back to Whitney.
- 2.
- 3.
Here and hereafter we use the term ‘restriction’ of objects on U p to ∂U p even though the map ∂U p → U p from the normalized boundary ∂U p may not be injective.
- 4.
To find a topology which is metrizable, we consider a support system \(\mathcal K\) and use the fact that \(\partial X = \bigcup \mathcal K_{\mathfrak p} \cap (s_{\mathfrak p}^{\partial })^{-1}(0)\) and [FOOO17, Proposition 2.11].
References
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Fukaya, K., Oh, YG., Ohta, H., Ono, K. (2020). Stokes’ Formula. In: Kuranishi Structures and Virtual Fundamental Chains. Springer Monographs in Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-15-5562-6_8
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DOI: https://doi.org/10.1007/978-981-15-5562-6_8
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