Approximating L^2 invariants of amenable covering spaces: A heat kernel approach

Abstract

In this paper, we prove that the L^2 Betti numbers of an amenable covering space can be approximated by the average Betti numbers of a regular exhaustion, under some hypotheses. We also prove that some L^2 spectral invariants can be approximated by the corresponding average spectral invariants of a regular exhaustion. The main tool which is used is a generalisation of the "principle of not feeling the boundary" (due to M. Kac), for heat kernels associated to boundary value problems.

14 pages, AMS-LaTeX, replaces an earlier version and contains a much strengthened version of one of the main results. 1991 Mathematics Subject Classification. 58G11, 58G18, 58G25

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