Twisting L2-invariants with finite-dimensional representations

Abstract

We investigate how one can twist [Formula: see text]-invariants such as [Formula: see text]-Betti numbers and [Formula: see text]-torsion with finite-dimensional representations. As a special case we assign to the universal covering [Formula: see text] of a finite connected [Formula: see text]-complex [Formula: see text] together with an element [Formula: see text] a [Formula: see text]-twisted [Formula: see text]-torsion function [Formula: see text], provided that the fundamental group of [Formula: see text] is residually finite and [Formula: see text] is [Formula: see text]-acyclic.