Residual Amenability and the Approximation of L^2-invariants
Abstract
Description
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.
13 pages, Latex2e
13 pages, Latex2e