Residual Amenability and the Approximation of L2-invariants
Abstract
We generalize Luck's Theorem to show that the L2-Betti numbers of a residually amenable covering space are the limit of the L2-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 L2 torsion is a homotopy invariant for such spaces. We give examples of residually amenable groups, including the Baumslag-Solitar groups.
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