Uniformly finite homology and amenable groups

Blank, Matthias; Diana, Francesca

doi:10.2140/agt.2015.15.467

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Uniformly finite homology and amenable groups

Matthias Blank and Francesca Diana

Algebraic & Geometric Topology 15 (2015) 467–492

DOI: 10.2140/agt.2015.15.467

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/

Volume 15, issue 1 (2015)