Abstract
In this chapter we prove Theorem 3.35 together with various addenda and variants.
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Notes
- 1.
In particular, \(Z_0^+ \subset \mathrm {Im}\psi _{\mathfrak p_0}\).
- 2.
Here we use the compatibility of parametrization with coordinate change, Definition 3.2 (4).
- 3.
See Definition 3.6 (3).
- 4.
We remark that \(\dim U_r = \dim U_{q_i^{\mathfrak p}} = U_{\mathfrak p_0} = \mathfrak d\) but \(\dim U_{p_n}\) may be smaller than \(\mathfrak d\).
- 5.
\(\varphi _{a;q\mathfrak p_0}\) is an embedding of Kuranishi chart in the strong sense (Definition 5.6 (3)) since the embedding \(\varphi _{a;q,\mathfrak p_0}\) is defined on the whole U(q).
- 6.
Compare Definition 7.52 (1)(b).
References
K. Fukaya, Y.-G. Oh, H. Ohta, K. Ono, Technical details on Kuranishi structure and virtual fundamental chain, arXiv:1209.4410
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, Y.-G. Oh, H. Ohta, K. Ono, Kuranishi structure, Pseudo-holomorphic curve, and Virtual fundamental chain; Part 1, arXiv:1503.07631v1
D. Joyce, D-manifolds and d-orbifolds: a theory of derived differential geometry, book manuscript
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Fukaya, K., Oh, YG., Ohta, H., Ono, K. (2020). Construction of Good Coordinate Systems. In: Kuranishi Structures and Virtual Fundamental Chains. Springer Monographs in Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-15-5562-6_11
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DOI: https://doi.org/10.1007/978-981-15-5562-6_11
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