Approximating $\ell_2$-Betti numbers of an amenable covering by ordinary Betti numbers

B. Eckmann

doi:10.1007/s000140050081

JournalscmhVol. 74, No. 1pp. 150–155

Approximating $ℓ_{2}$ -Betti numbers of an amenable covering by ordinary Betti numbers

B. Eckmann
Eidgenössische Technische Hochschule, Zürich, Switzerland

$Approximating $\ell_2$-Betti numbers of an amenable covering by ordinary Betti numbers cover$

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Abstract

It is shown that the $ℓ_{2}$ -Betti numbers of an amenable covering of a finite cell-complex can be approximated by ordinary Betti numbers of the finite Fmlner subcomplexes. This is a new proof, using simple homological arguments, of a recent result of Dodziuk and Mathai.

Cite this article

B. Eckmann, Approximating $ℓ_{2}$ -Betti numbers of an amenable covering by ordinary Betti numbers. Comment. Math. Helv. 74 (1999), no. 1, pp. 150–155

DOI 10.1007/S000140050081