Kuranishi structure, Pseudo-holomorphic curve, and virtual fundamental chain: Part 2

Abstract: This article is the second part of the article we promised to write at the end of Section 1 of FOOO15. (Part I appeared in Part I.) We discuss the foundation of the virtual fundamental chain and cycle technique, especially its version that appeared in [FOn] and also in Section A1, Section 7.5 [FOOO4], Section 12 [FOOO7], [Fu2]. This article is independent of our earlier writing [FOOO15]. We also do not assume that the readers have any knowledge on the pseudo-holomorphic curve. In this second part, we consider a system of spaces with Kuranishi structures (abbreviated as a K-system) and its simultaneous perturbations.