Reidemeister torsion in generalized Morse theory

TL;DR

This paper proves that a Reidemeister torsion invariant for Morse theory of closed 1-forms is topologically invariant, potentially serving as a foundation for future generalizations to Floer theory.

Contribution

It provides an a priori proof that the Reidemeister torsion in generalized Morse theory is a topological invariant, advancing the theoretical understanding of Morse and Floer theories.

Findings

Reidemeister torsion is a topological invariant in this setting

The proof is established a priori, without relying on specific computations

Lays groundwork for extending these ideas to Floer theory

Abstract

In two previous papers with Yi-Jen Lee, we defined and computed a notion of Reidemeister torsion for the Morse theory of closed 1-forms on a finite dimensional manifold. The present paper gives an a priori proof that this Morse theory invariant is a topological invariant. It is hoped that this will provide a model for possible generalizations to Floer theory.