Commentarii Mathematici Helvetici


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Volume 74, Issue 1, 1999, pp. 150–155
DOI: 10.1007/s000140050081

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

B. Eckmann[1]

(1) Departement Mathematik, Eidgenössische Technische Hochschule, Rämistr. 101, 8092, ZÜRICH, SWITZERLAND

It is shown that the $\ell_2$-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.

Keywords: Amenable groups, covering spaces, l 2 -homology, Betti numbers

Eckmann B.: Approximating $\ell_2$-Betti numbers of an amenable covering by ordinary Betti numbers. Comment. Math. Helv. 74 (1999), 150-155. doi: 10.1007/s000140050081