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

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.

arXiv comment102+2 pages

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• Open string instantons and superpotentials
• Dirichlet branes, homological mirror symmetry, and stability
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Cited by in corpus (4)

• Azumaya-type noncommutative spaces and morphisms therefrom: Polchinski's D-branes in string theory from Grothendieck's viewpoint
• On a proof of the Labastida-Marino-Ooguri-Vafa conjecture
• Azumaya noncommutative geometry and D-branes - an origin of the master nature of D-branes
• Relatively Open Gromov-Witten Invariants for Symplectic Manifolds of Lower Dimensions