JournalscmhVol. 74 , No. 1DOI 10.1007/s000140050081

Approximating 2\ell_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

Abstract

It is shown that the 2\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.