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

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

1996-09-06

arxiv.org/abs/dg-ga/9609002v2

Mathematics

Differential Geometry

14 pages, AMS-LaTeX, replaces an earlier version and contains a much strengthened version of one of the main results. 1991 Mat

Scientific paper

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.

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