On the anomaly terms in Cheeger-M\"uller theorem on spaces with conical singularities

TL;DR

This paper investigates the anomaly term in the Cheeger-Müller theorem for spaces with conical singularities, showing it vanishes in smooth cases but is non-trivial for cones over tori, revealing nuanced geometric behavior.

Contribution

It demonstrates the conditions under which the anomaly term vanishes or remains non-trivial in spaces with conical singularities, extending understanding of torsion invariants.

Findings

Anomaly term vanishes in smooth cases

Anomaly term is non-trivial for cones over tori

Provides insight into torsion invariants in singular spaces

Abstract

We prove that the anomaly term appearing in the ratio between Reidemeister torsion and analytic torsion for a space with a conical singularity vanishes in the smooth case. Moreover, we show that such anomaly term is non trivial for the cone over a torus.