The $L^2$-torsion for representations of hyperbolic lattices

Abstract

We prove equality of analytic and topological $L^2$-torsion associated with an odd-dimensional finite volume hyperbolic manifold and a representation of the fundamental group which extends to the ambient Lie group. This generalizes a previous result due to Lück and Schick. Alternatively, this result can be regarded as the $L^2$-analogue of recent work by Müller and Rochon.

35 pages, 3 figures