Various L2-signatures and a topological L2-signature theorem

Details Various L2-signatures and a topological L2-signature theorem Various L2-signatures and a topological L2-signature theorem

2002-09-13

arxiv.org/abs/math/0209161v3

High-dimensional manifold topology, Proceedings of the school held in Trieste, May 21--June 8, 2001. Edited by F. T. Farrell a

Mathematics

Geometric Topology

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Scientific paper

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 Poincar 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.

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