Communications in Analysis and Geometry

Volume 30 (2022)

Number 3

Flat vector bundles and analytic torsion on orbifolds

Pages: 575 – 656



Shu Shen (Institut de Mathématiques de Jussieu-Paris Rive Gauche, Sorbonne Université, Paris, France)

Jianqing Yu (School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui, China)


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 determinant 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 reductive type, which extends one of the results obtained by the first author for compact locally symmetric manifolds.

Received 3 September 2018

Accepted 3 September 2019

Published 14 December 2022