Open Gromov–Witten invariants, mirror maps, and Seidel representations for toric manifolds

@article{Chan2017OpenGI,
  title={Open Gromov–Witten invariants, mirror maps, and Seidel representations for toric manifolds},
  author={K. Chan and Siu-Cheong Lau and N. Leung and Hsian-hua Tseng},
  journal={Duke Mathematical Journal},
  year={2017},
  volume={166},
  pages={1405-1462}
}
Let $X$ be a compact toric K\"ahler manifold with $-K_X$ nef. Let $L\subset X$ be a regular fiber of the moment map of the Hamiltonian torus action on $X$. Fukaya-Oh-Ohta-Ono defined open Gromov-Witten (GW) invariants of $X$ as virtual counts of holomorphic discs with Lagrangian boundary condition $L$. We prove a formula which equates such open GW invariants with closed GW invariants of certain $X$-bundles over $\mathbb{P}^1$ used to construct the Seidel representations for $X$. We apply this… Expand
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