Volume 15, issue 1 (2015)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Uniformly finite homology and amenable groups

Matthias Blank and Francesca Diana

Algebraic & Geometric Topology 15 (2015) 467–492
Abstract

Uniformly finite homology is a coarse invariant for metric spaces; in particular, it is a quasi-isometry invariant for finitely generated groups. In this article, we study uniformly finite homology of finitely generated amenable groups and prove that it is infinite-dimensional in many cases. The main idea is to use different transfer maps to distinguish between classes in uniformly finite homology. Furthermore we show that there are infinitely many classes in degree zero that cannot be detected by means.

Keywords
amenable groups, uniformly finite homology
Mathematical Subject Classification 2010
Primary: 20J05
Secondary: 43A07
References
Publication
Received: 5 June 2014
Accepted: 28 July 2014
Published: 23 March 2015
Authors
Matthias Blank
Fakultät für Mathematik
Universität Regensburg
93040 Regensburg
Germany
http://www.mathematik.uni-r.de/blank/
Francesca Diana
Fakultät für Mathematik
Universität Regensburg
93040 Regensburg
Germany
http://homepages-nw.uni-regensburg.de/~dif13273/