Degeneration and gluing of Kuranishi structures in Gromov-Witten theory and the degeneration/gluing axioms for open Gromov-Witten invariants under a symplectic cut

TL;DR

This paper investigates how Kuranishi structures degenerate and can be glued in Gromov-Witten theory under symplectic cuts, establishing axioms for open invariants and connecting different degeneration formulas.

Contribution

It introduces degeneration and gluing axioms for open Gromov-Witten invariants, advancing the construction of virtual fundamental chains through specialization.

Findings

Established degeneration and gluing axioms for open Gromov-Witten invariants.

Connected degeneration formulas of closed Gromov-Witten invariants by different authors.

Provided a framework for constructing virtual fundamental chains via specialization.

Abstract

We study the degeneration and the gluing of Kuranishi structures in Gromov-Witten theory under a symplectic cut. This leads us to a degeneration axiom and a gluing axiom for open Gromov-Witten invariants. They provide then a route to the construction of virtual fundamental chains via specialization. Comments on the equivalence of the degeneration formula of closed Gromov-Witten invariants by Li-Ruan/Li versus Ionel-Parker are given in the Appendix.