Lück W. and Schick, T.: Various L2-signatures and a topological L2-signature theorem

Autor: Wolfgang Lück , Thomas Schick
Titel: Various L2-signatures and a topological L2-signature theorem (dvi) (pdf)
High-dimensional manifold topology, 362--399, World Sci. Publishing, River Edge, NJ, 2003

Abstract: For a normal covering over a closed oriented topological manifold we give a proof of the L2-signature theorem with twisted coefficients, using Lipschitz structures and the Lipschitz signature operator introduced by Teleman. We also prove that the L-theory isomorphism conjecture as well as the C^*_max-version of the Baum-Connes conjecture imply the L2-signature theorem for a normal covering over a Poincaré space, provided that the group of deck transformations is torsion-free. We discuss the various possible definitions of L2-signatures (using the signature operator, using the cap product of differential forms, using a cap product in cellular L2-cohomology,...) in this situation, and prove that they all coincide.

Thomas Schick