#### Volume 9, issue 4 (2009)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 Author Index To Appear Other MSP Journals
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
##### 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