Abstract
Let X be a paracompact metrizable space, and let \(\widehat {\mathcal U} = (\{\mathcal U_p\},\{\Phi _{pq}\})\) be a Kuranishi structure on it.
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Notes
- 1.
- 2.
See Definition 3.5 for this notation.
- 3.
By definition, KG-embedding \(\widehat {\Phi ^1}\) is a strict KG-embedding from an open substructure \({\widehat {\mathcal U}'}\) of \({\widehat {\mathcal U}}\). \({\widehat {\mathcal U_0}}\) is taken as an open substructure of \({\widehat {\mathcal U}'}\). So the composition of
and 
is defined.
and 
is defined.References
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K. Fukaya, Y.-G. Oh, H. Ohta, K. Ono, Shrinking good coordinate systems associated to Kuranishi structures. J. Symplectic Geom. 14(4), 1295–1310 (2016), arXiv:1405.1755
K. Fukaya, K. Ono, Arnold conjecture and Gromov–Witten invariant. Topology 38(5), 933–1048 (1999)
D. Yang, The Polyfold-Kuranishi Correspondence I: A Choice-independent Theory of Kuranishi Structures, arXiv:1402.7008
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Fukaya, K., Oh, YG., Ohta, H., Ono, K. (2020). Thickening of a Kuranishi Structure. In: Kuranishi Structures and Virtual Fundamental Chains. Springer Monographs in Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-15-5562-6_5
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