Twisted $L^2$-torsion on the character variety

Léo Bénard, Jean Raimbault

Published 2020-09-14Version 1

We define a twisted $L^2$-torsion on the character variety of 3-manifold $M$ and study some of its properties. In the case where $M$ is hyperbolic of finite volume, we prove that the $L^2$-torsion is a real analytic function on a neighborhood of any lift of the holonomy representation.