Uniformly finite homology and amenable groups

Blank, Matthias¹ ; Diana, Francesca¹

¹Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany

Algebraic and Geometric Topology, Tome 15 (2015) no. 1, pp. 467-492

Résumé

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.

Détail

DOI : 10.2140/agt.2015.15.467

Classification : 20J05, 43A07
Keywords: amenable groups, uniformly finite homology

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