Reidemeister torsion for flat superconnections

TL;DR

This paper introduces a new approach to defining Reidemeister torsion for flat superconnections using higher parallel transport, aiming to unify combinatorial and analytic torsion theories.

Contribution

It applies the integration A_{infty}-functor to define Reidemeister torsion for flat superconnections, potentially generalizing the Cheeger-Mueller Theorem.

Findings

Proposes a new definition of Reidemeister torsion for superconnections

Suggests a possible equivalence between combinatorial and analytic torsion

Lays groundwork for extending classical torsion theorems to superconnection context

Abstract

We use higher parallel transport -- more precisely, the integration A_{infty}-functor constructed by Block-Smith and Arias Abad-Schaetz -- to define Reidemeister torsion for flat superconnections. We hope that the combinatorial Reidemeister torsion coincides with the analytic torsion defined by Mathai and Wu, thus permitting for a generalization of the Cheeger-Mueller Theorem.