# 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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