Comparison between two analytic torsions on orbifolds

TL;DR

This paper proves an equality between two types of analytic torsion on orbifolds with isolated conical singularities, extending the understanding of spectral invariants in singular geometric settings.

Contribution

It establishes a precise relationship between Dar's analytic torsion and Ma's orbifold analytic torsion on certain singular orbifolds, under specific bundle assumptions.

Findings

Equality between Dar's and Ma's analytic torsions on orbifolds.

Extension of analytic torsion concepts to orbifolds with conical singularities.

Clarification of conditions under which the torsions coincide.

Abstract

In this paper, we establish an equality between the analytic torsion introduced by Dar\cite{MR876230} and the orbifold analytic torsion defined by Ma \cite{MR2140438} on a compact manifold with isolated conical singularities which in addition has an orbifold structure. We assume the orbifold flat vector bundle is an honest vector bundle, although the metric on the flat bundle may not be flat.