Open AccessApproximating $\ell_2$ -Betti numbers of an amenable covering by ordinary Betti numbers
Author(s) -
Beno Eckmann
Publication year - 1999
Publication title -
commentarii mathematici helvetici
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.603
H-Index - 46
eISSN - 1420-8946
pISSN - 0010-2571
DOI - 10.1007/s000140050081
Subject(s) - betti number , mathematics , simple (philosophy) , combinatorics , pure mathematics , discrete mathematics , epistemology , philosophy
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 Fœlner subcomplexes. This is a new proof, using simple homological arguments, of a recent result of Dodziuk and Mathai.
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