Flat vector bundles and analytic torsion on orbifolds (Q2108540)

This articles presents three main results related to flat orbifold vector bundles. Firstly, the authors presented a bijection between the isomorphic classes of complex proper flat orbifold vector bundles and the equivalence classes of complex representations of the orbifold fundamental group. Secondly, they studied the Ray-Singer metrics and proved a Bismut-Zhang anomaly formula [\textit{J.-M. Bismut} and \textit{W. Zhang}, An extension of a theorem by Cheeger and Müller. With an appendix by François Laudenbach. Paris: Société Mathématique de France (1992; Zbl 0781.58039)] for compact orbifolds. Thirdly, they proved a conjecture from \textit{D. Fried} [Invent. Math. 84, 523--540 (1986; Zbl 0621.53035)] about the equality between the analytic torsion and the zero value of the Ruelle dynamical zeta function. The authors extend Fried's result to a general compact odd dimensional locally symmetric orbifold of the reductive type.