Comparison between two analytic torsions on orbifolds

Abstract

In this paper, we establish an equality between the analytic torsion introduced by Dar (Math Z 194(2): 193–216, 1987) and the orbifold analytic torsion defined by Ma (Trans Am Math Soc 357(6): 2205–2233, 2005) on an even dimensional 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.