Approximating L^2 invariants of amenable covering spaces: A heat kernel approach
dg-ga
2008-02-03 v2 Differential Geometry
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.
Cite
@article{arxiv.dg-ga/9609002,
title = {Approximating L^2 invariants of amenable covering spaces: A heat kernel approach},
author = {Jozef Dodziuk and Varghese Mathai},
journal= {arXiv preprint arXiv:dg-ga/9609002},
year = {2008}
}
Comments
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