Volume 9, issue 4 (2009)

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Thompson's group $F$ and uniformly finite homology

Daniel Staley

Algebraic & Geometric Topology 9 (2009) 2349–2360
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