{
  "id": "1310.4395",
  "version": "v3",
  "published": "2013-10-16T14:20:33.000Z",
  "updated": "2021-09-14T13:03:37.000Z",
  "title": "Non-amenability of R.Thompson's group F",
  "authors": [
    "Azer Akhmedov"
  ],
  "comment": "45 pages, 4 figures. Comments are welcome! arXiv admin note: substantial text overlap with arXiv:0902.3849",
  "categories": [
    "math.GR",
    "math.DS"
  ],
  "abstract": "We present a proof of non-amenability of R.Thompson's group F.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-12-20T16:47:50.000Z",
      "abstract": "We present a short proof of non-amenability of R.Thompson's group F.",
      "comment": "This paper has been withdrawn by the author; This paper has been withdrawn - the corresponding version of condition $\\dagger_4$ from the previous version (arXiv:0902.3849) is needed in the statement. I have deleted this condition trying to capture the content of it in the simplified conditions, but has done it carelessly enough that new conditions allow, as the referee pointed out, trivial words in F. The proof of Prop.5.3. is written with this extra condition in mind. Relaxing the conditions allows more space for the trees, which is needed. The essence of the problem in our approach is in the possibility that the trees may travel long without becoming successful in a uniform fashion. In this new version, and in the old version, we have been unable to resolve this serious issue. It is hard to say if there is any chance for the approach to succeed",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2021-09-14T13:03:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "thompsons group",
      "non-amenability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.4395A"
    }
  }
}