Let be a compact toric Kähler manifold with nef. Let be a regular fiber of the moment map of the Hamiltonian torus action on . Fukaya, Oh, Ohta, and Ono defined open Gromov–Witten (GW) invariants of as virtual counts of holomorphic disks with Lagrangian boundary condition . We prove a formula that equates such open GW invariants with closed GW invariants of certain -bundles over used by Seidel and McDuff earlier to construct Seidel representations for . We apply this formula and degeneration techniques to explicitly calculate all these open GW invariants. This yields a formula for the disk potential of , an enumerative meaning of mirror maps, and a description of the inverse of the ring isomorphism of Fukaya, Oh, Ohta, and Ono.
"Open Gromov–Witten invariants, mirror maps, and Seidel representations for toric manifolds." Duke Math. J. 166 (8) 1405 - 1462, 1 June 2017. https://doi.org/10.1215/00127094-0000003X