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

TL;DR

This paper establishes the equality of analytic and topological $L^2$-torsion for certain hyperbolic manifolds and group representations, extending previous results and connecting to recent work in the field.

Contribution

It generalizes prior results by proving the equality of analytic and topological $L^2$-torsion for a broader class of hyperbolic manifolds and representations.

Findings

Proves equality of analytic and topological $L^2$-torsion for hyperbolic manifolds.

Extends previous results by L"uck and Schick.

Connects $L^2$-torsion theory with recent work by M"uller and Rochon.

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 L\"uck and Schick. Alternatively, this result can be regarded as the $L^2$-analogue of recent work by M\"uller and Rochon.