Residual Amenability and the Approximation of L^2-invariants
dg-ga
2007-05-23 v1 Differential Geometry
Abstract
We generalize Luck's Theorem to show that the L^2-Betti numbers of a residually amenable covering space are the limit of the L^2-Betti numbers of a sequence of amenable covering spaces. We show that any residually amenable covering space of a finite simplicial complex is of determinant class, and that the L^2 torsion is a homotopy invariant for such spaces. We give examples of residually amenable groups, including the Baumslag-Solitar groups.
Cite
@article{arxiv.dg-ga/9710002,
title = {Residual Amenability and the Approximation of L^2-invariants},
author = {Bryan Clair},
journal= {arXiv preprint arXiv:dg-ga/9710002},
year = {2007}
}
Comments
13 pages, Latex2e