Burghelea-Haller analytic torsion for twisted de Rham complexes

TL;DR

This paper extends the Burghelea-Haller analytic torsion to twisted de Rham complexes and compares it with Huang's twisted refined analytic torsion, advancing the understanding of torsion invariants in differential geometry.

Contribution

It introduces an extension of Burghelea-Haller torsion to twisted complexes and provides a comparison with existing twisted refined torsion.

Findings

Extended Burghelea-Haller torsion to twisted complexes

Compared new torsion with Huang's twisted refined torsion

Enhanced understanding of torsion invariants in geometry

Abstract

In this paper, we extend the Burghelea-Haller analytic torsion to the twisted de Rham complexes. We also compare it with the twisted refined analytic torsion defined by Huang.