Gromov-Witten invariants of log Calabi-Yau 3-folds are holomorphic lagrangian correspondences

Abstract

We introduce a holomorphic version of Weinstein's symplectic category, in which objects are holomorphic symplectic manifolds, and morphisms are holomorphic lagrangian correspondences. We then extend this category to log schemes, and prove that Gromov-Witten invariants of log Calabi-Yau 3-folds are naturally encoded as holomorphic lagrangian correspondences. Gromov-Witten invariants and Donaldson-Thomas invariants are then conjecturally related by a natural unitary lagrangian correspondence.