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

摘要

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