Residual Amenability and the Approximation of L 2 -invariants

We generalize Lück’s Theorem to show that the L-Betti numbers of a residually amenable covering space are the limit of the L-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 torsion is a homotopy invariant for such spaces. We… (More)