Quantum Reidemeister torsion, open Gromov-Witten invariants and a spectral sequence of Oh

Abstract

We adapt classical Reidemeister torsion to monotone Lagrangian submanifolds using the pearl complex of Biran and Cornea. The definition involves generic choices of data and we identify a class of Lagrangians for which this torsion is invariant and can be computed in terms of genus zero open Gromov-Witten invariants. This class is defined by a vanishing property of a spectral sequence of Oh in Lagrangian Floer theory.

V3: Replaced a freeness assumption on the homology of the Lagrangians for one on the cardinality of torsion. After referee reports: many cosmetic changes, clarified hypotheses, added a section on open Gromov-Witten invariants. V2: We shift viewpoint in this second version to consider a more general class of Lagrangians than just tori. Rewrote the whole paper accordingly