On a twisted Reidemeister torsion

TL;DR

This paper introduces a new twisted Reidemeister torsion for finite simplicial complexes, extending previous definitions by incorporating twisted cochains and utilizing currents, with potential applications in topology.

Contribution

It defines a novel twisted Reidemeister torsion for simplicial complexes using currents, expanding the theoretical framework of torsion invariants.

Findings

Defines a twisted Reidemeister torsion for simplicial complexes.

Extends previous torsion definitions by Mathai and Wu.

Utilizes Dupont's currents to construct the torsion.

Abstract

Given a finite simplicial complex, a unimodular representation of its fundamental group and a closed twisted cochain of odd degree, we define a twisted version of the Reidemeister torsion, extending a previous definition of V. Mathai and S. Wu. The main tool is a complex of piecewise smooth currents, defined by J. Dupont.