Open GW theory on symplectic manifolds and symplectic cutting

Abstract

Let $(X,\om)$ be a symplectic manifold and $L$ be a Lagrangian submanifold diffeomorphic to $S^n$, $\mathbb{R}{\P }^n$, or a Lens space of a certain type. Using the symplectic cut and symplectic sum constructions, we express the open Gromov-Witten invariants of $(X,L)$ in terms of open Gromov-Witten invariants of a pair $(X_{-},L)$ determined by $L$ and the standard Gromov-Witten invariants of a symplectic manifold $X_{+}$ determined by $(X,L)$. We also describe other applications of this approach.

References in corpus (3)

• Disk Instantons, Mirror Symmetry and the Duality Web
• Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions
• Open strings, Lagrangian conductors and Floer functor