{
  "id": "0806.2877",
  "version": "v2",
  "published": "2008-06-17T22:02:45.000Z",
  "updated": "2009-03-11T03:39:52.000Z",
  "title": "Thompson's Group F and Uniformly Finite Homology",
  "authors": [
    "Dan Staley"
  ],
  "comment": "pdfLaTex, 17 pages, 11 figures",
  "categories": [
    "math.GR"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-03-11T03:39:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65"
    ],
    "keywords": [
      "thompsons group",
      "paper demonstrates",
      "cayley graph",
      "measure zero",
      "uniformly finite homology"
    ],
    "note": {
      "typesetting": "PDFLaTeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0806.2877S"
    }
  }
}