Mathematical Research Letters

Volume 22 (2015)

Number 3

Gross-Siebert’s slab functions and open GW invariants for toric Calabi-Yau manifolds

Pages: 881 – 898



Siu-Cheong Lau (Department of Mathematics, Harvard University, Cambridge, Massachusetts, U.S.A.)


This paper derives an equality between the slab functions in Gross–Siebert program and generating functions of open Gromov–Witten invariants for toric Calabi–Yau manifolds, and thereby confirms a conjecture of Gross–Siebert on symplectic enumerative meaning of slab functions. The proof is based on the open mirror theorem of Chan–Cho–Lau–Tseng. It shows an instance of correspondence between tropical and symplectic geometry in the open sector.

Accepted 4 December 2014

Published 20 May 2015