Thompson’s group F and uniformly finite homology

Staley, Daniel

doi:10.2140/agt.2009.9.2349

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Thompson's group $F$ and uniformly finite homology

Daniel Staley

Algebraic & Geometric Topology 9 (2009) 2349–2360

DOI: 10.2140/agt.2009.9.2349

Abstract

We use the uniformly finite homology developed by Block and Weinberger to study the geometry of the Cayley graph of Thompson’s group $F$ . In particular, a certain class of subgraph of $F$ is shown to be nonamenable (in the Følner sense). This shows that if the Cayley graph of $F$ is amenable, these subsets, which include every finitely generated submonoid of the positive monoid of $F$ , must necessarily have measure zero.

Keywords

Thompson's group F, uniformly finite homology, amenability

Mathematical Subject Classification 2010

Primary: 20F65, 05C25

Secondary: 43A07

References

Publication

Received: 3 July 2008

Revised: 1 September 2009

Accepted: 27 September 2009

Published: 31 October 2009

Authors

Daniel Staley
Department of Mathematics Rutgers University 110 Frelinghuysen Road Piscataway NJ 08854-8019 USA
http://math.rutgers.edu/~staley

Volume 9, issue 4 (2009)