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Residual Amenability and the Approximation of L^2-invariants

Bryan Clair
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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.

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BibTeXRIS

Bryan Clair. 1997-10-03. Residual Amenability and the Approximation of L^2-invariants. https://arxiv.org/abs/dg-ga/9710002

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