Families torsion and Morse functions for covering spaces

TL;DR

This paper extends the Cheeger-Müller theorem to $L^2$-analytic torsion forms for covering spaces, assuming a fiberwise Morse function exists and the Novikov-Shubin invariant is positive, advancing the understanding of torsion invariants.

Contribution

It proves the Cheeger-Müller theorem for $L^2$-analytic torsion forms under new conditions involving fiberwise Morse functions and Novikov-Shubin invariants.

Findings

Established the Cheeger-Müller theorem for $L^2$-analytic torsion forms

Identified conditions involving fiberwise Morse functions and Novikov-Shubin invariants

Extended the applicability of torsion invariants to covering spaces

Abstract

In this paper we prove the Cheeger-M\"{u}ller theorem for $L^2$-analytic torsion form under the assumption that there exists a fiberwise Morse function and the Novikov-Shubin invariant is positive.