Construction of Kuranishi structures on the moduli spaces of pseudo holomorphic disks: II

Abstract: This is the second of a series of two articles in which we provide detailed and self-contained account of the construction of a system of Kuranishi structures on the moduli spaces of pseudo holomorphic disks. Using the notion of obstruction bundle data introduced in [FOOO8], we give a systematic way of constructing a system of Kuranishi structures on the moduli spaces of pseudo holomorphic disks which are compatible at the boundary and corners. More specifically, it defines a tree like K-system in the sense of [FOOO6, Definition 21.9]. The method given in this paper does not only simplify the description of the constructions in the earlier literature, but also is designed to provide a systematic utility tool for the construction of a system of Kuranishi structures in the future research. We also establish its uniqueness.