From good coordinate systems to kuranishi structures and back with cf-perturbations

Abstract

As we explained at the end of Chap. 4, it is more canonical to define the notion of fiber products of spaces with Kuranishi structure than to define that of fiber products of spaces with a good coordinate system. On the other hand, in Chap. 7, we gave the definition of CF-perturbation and of the pushout of differential forms via good coordinate systems. In this chapter, we describe how we go from a good coordinate system to a Kuranishi structure and back together with CF-perturbations on them, and prove in Theorem 9.14 that we can define the pushout via the Kuranishi structure itself in such a way that the outcome is independent of the auxiliary choice of good coordinate system. © Springer Nature Singapore Pte Ltd 2020.