arXiv Analytics

Sign in

arXiv:0806.2877 [math.GR]AbstractReferencesReviewsResources

Thompson's Group F and Uniformly Finite Homology

Dan Staley

Published 2008-06-17, updated 2009-03-11Version 2

This paper demonstrates the uniformly finite homology developed by Block and Weinberger and its relationship to amenable spaces via applications to the Cayley graph of Thompson's Group F. In particular, a certain class of subgraph of F is shown to be non-amenable. This shows that if F is amenable, these subsets (which include every finitely generated submonoid of the positive monoid of F) must necessarily have measure zero.

Comments: pdfLaTex, 17 pages, 11 figures
Categories: math.GR
Subjects: 20F65
Related articles: Most relevant | Search more
arXiv:math/0208117 [math.GR] (Published 2002-08-14)
Combinatorial properties of Thompson's group F
arXiv:2210.12304 [math.GR] (Published 2022-10-21)
Cayley graphs of R. Thompson's group F: new estimates for the density
arXiv:0902.0202 [math.GR] (Published 2009-02-02, updated 2010-02-19)
Counting elements and geodesics in Thompson's group $F$

Links

Toolbox