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

TL;DR

This paper extends Reidemeister torsion to certain monotone Lagrangian submanifolds using pearl complexes, linking it to genus zero open Gromov-Witten invariants via a spectral sequence in Floer theory.

Contribution

It introduces a new invariant for monotone Lagrangians, computed through open Gromov-Witten invariants, and identifies conditions for its invariance related to Oh's spectral sequence.

Findings

Reidemeister torsion adapted to monotone Lagrangians.

Invariant torsion expressed via genus zero open Gromov-Witten invariants.

Spectral sequence vanishing characterizes the class of Lagrangians with invariant torsion.

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.