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2009 Thompson's group $F$ and uniformly finite homology
Daniel Staley
Algebr. Geom. Topol. 9(4): 2349-2360 (2009). 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.

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Daniel Staley. "Thompson's group $F$ and uniformly finite homology." Algebr. Geom. Topol. 9 (4) 2349 - 2360, 2009. https://doi.org/10.2140/agt.2009.9.2349

Information

Received: 3 July 2008; Revised: 1 September 2009; Accepted: 27 September 2009; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1172.05325
MathSciNet: MR2558313
Digital Object Identifier: 10.2140/agt.2009.9.2349

Subjects:
Primary: 05C25, 20F65
Secondary: ‎43A07‎

Rights: Copyright © 2009 Mathematical Sciences Publishers

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