Gauss-Manin connection in disguise: Open Gromov-Witten invariants

Abstract

In mirror symmetry, after the work by J. Walcher, the number of holomorphic disks with boundary on the real quintic lagrangian in a general quintic threefold is related to the periods of the mirror quintic family with boundary on two homologous rational curves. Following the ideias of H.Movasati, we construct a quasi-affine space parametrizing such objects enhanced with a frame for the relative de Rham cohomology with boundary at the curves compatible with the mixed Hodge structure. We also compute a modular vector field attached to such a parametrization.