Monotone Lagrangian Floer theory in smooth divisor complements: II

TL;DR

This paper establishes the existence of Kuranishi structures on RGW compactifications of moduli spaces of holomorphic discs and strips in smooth divisor complements, enabling Floer homology for monotone Lagrangians.

Contribution

It proves that RGW compactifications admit Kuranishi structures, a key step for constructing Floer homology in this geometric setting.

Findings

RGW compactifications admit Kuranishi structures

Foundation for Floer homology in divisor complements established

Advances understanding of moduli spaces in symplectic geometry

Abstract

In the first part of the present series of papers, we studied the moduli spaces of holomorphic discs and strips into an open symplectic manifold, isomorphic to the complement of a smooth divisor in a closed symplectic manifold. In particular, we introduced a compactification of this moduli space, which is called the RGW compactification. The goal of this paper is to show that the RGW compactifications admit Kuranishi structures. This result provides the crucial ingredient for the main construction of this series of papers: Floer homology for monotone Lagrangians in a smooth divisor complement.