An extension of the Cheeger-M\"uller theorem for a cone

TL;DR

This paper extends the Cheeger-Müller theorem to even-dimensional finite metric cones over odd-dimensional manifolds, establishing a new equality between $L^2$-analytic torsion and intersection R torsion.

Contribution

It generalizes the Cheeger-Müller theorem to a broader class of geometric spaces, specifically finite metric cones.

Findings

Proves the equality of $L^2$-analytic torsion and intersection R torsion for cones.

Extends the theoretical framework of torsion invariants to singular spaces.

Abstract

We prove the equality of the $L^2$-analytic torsion and the intersection R torsion of the even dimensional finite metric cone over an odd dimensional compact manifold.