Flat vector bundles and analytic torsion on orbifolds

Abstract

This article is devoted to a study of flat orbifold vector bundles. We construct a bijection between the isomorphic classes of proper flat orbifold vector bundles and the equivalence classes of representations of the orbifold fundamental groups of base orbifolds. We establish a Bismut-Zhang like anomaly formula for the Ray-Singer metric on the determine line of the cohomology of a compact orbifold with coefficients in an orbifold flat vector bundle. We show that the analytic torsion of an acyclic unitary flat orbifold vector bundle is equal to the value at zero of a dynamical zeta function when the underlying orbifold is a compact locally symmetric space of the reductive type, which extends one of the results obtained by the first author for compact locally symmetric manifolds.

Final version. Accepted by Comm. Anal. Geom on Sep 3, 2019

References in corpus (1)

• Ruelle zeta function at zero for surfaces

Cited by in corpus (4)

• Analytic torsion, dynamical zeta function, and the Fried conjecture for admissible twists
• Morse-Smale flow, Milnor metric, and dynamical zeta function
• The twisted Ruelle zeta function on compact hyperbolic orbisurfaces and Reidemeister-Turaev torsion
• On full asymptotics of analytic torsions for compact locally symmetric orbifolds