{
  "id": "1112.1942",
  "version": "v6",
  "published": "2011-12-08T20:51:45.000Z",
  "updated": "2012-11-25T11:03:31.000Z",
  "title": "The classification theorem for groups of homeomorphisms of the line. Nonamenability of Thompson's group $F$",
  "authors": [
    "Leva Beklaryan"
  ],
  "comment": "This paper has been withdrawn by the author due to a crucial error in Theorem B*",
  "categories": [
    "math.GR",
    "math.DS"
  ],
  "abstract": "This paper allows one to obtain a criterion for the existence of a projectively invariant measure formulated in terms of combinatorial properties of a group (amenability of some canonical quotient group). Such necessary and sufficient condition is a basis of the classification scheme for groups of homeomorphisms of the line. In particular, a nonamenability of Thompson's group $F$ follows from the obtained criterion.",
  "revisions": [
    {
      "version": "v6",
      "updated": "2012-11-25T11:03:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20Exx"
    ],
    "keywords": [
      "thompsons group",
      "classification theorem",
      "homeomorphisms",
      "nonamenability",
      "projectively invariant measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.1942B"
    }
  }
}