On the homotopy invariance of L^2 torsion for covering spaces

Abstract

We prove the homotopy invariance of L^2 torsion for covering spaces, whenever the covering transformation group is either residually finite or amenable. In the case when the covering transformation group is residually finite and when the L^2 cohomology of the covering space vanishes, the homotopy invariance was established earlier by Lueck. We also give some applications of our results.