{
  "id": "math/0204249",
  "version": "v1",
  "published": "2002-04-19T18:06:37.000Z",
  "updated": "2002-04-19T18:06:37.000Z",
  "title": "Thompson's group F is not almost convex",
  "authors": [
    "Sean Cleary",
    "Jennifer Taback"
  ],
  "comment": "19 pages, 7 figures",
  "categories": [
    "math.GR"
  ],
  "abstract": "We show that Thompson's group F does not satisfy Cannon's almost convexity condition AC(n) for any integer n in the standard finite two generator presentation. To accomplish this, we construct a family of pairs of elements at distance n from the identity and distance 2 from each other, which are not connected by a path lying inside the n-ball of length less than k for increasingly large k. Our techniques rely upon Fordham's method for calculating the length of a word in F and upon an analysis of the generators' geometric actions on the tree pair diagrams representing elements of F.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-04-19T18:06:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65"
    ],
    "keywords": [
      "thompsons group",
      "tree pair diagrams representing elements",
      "convexity condition ac",
      "geometric actions",
      "fordhams method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......4249C"
    }
  }
}