Refined analytic torsion

Abstract

Given an acyclic representation $\alpha$ of the fundamental group of a compact oriented odd-dimensional manifold, which is close enough to an acyclic unitary representation, we define a refinement $T_\alpha$ of the Ray-Singer torsion associated to $\alpha$, which can be viewed as the analytic counterpart of the refined combinatorial torsion introduced by Turaev. $T_\alpha$ Show more