{
  "id": "0710.4152",
  "version": "v2",
  "published": "2007-10-22T21:05:45.000Z",
  "updated": "2009-04-28T22:19:48.000Z",
  "title": "Unsigned state models for the Jones polynomial",
  "authors": [
    "Iain Moffatt"
  ],
  "comment": "Minor corrections. To appear in Annals of Combinatorics",
  "journal": "Ann. Comb., 15 (2011) 127-146",
  "doi": "10.1007/s00026-011-0087-4",
  "categories": [
    "math.GT",
    "math.CO"
  ],
  "abstract": "It is well a known and fundamental result that the Jones polynomial can be expressed as Potts and vertex partition functions of signed plane graphs. Here we consider constructions of the Jones polynomial as state models of unsigned graphs and show that the Jones polynomial of any link can be expressed as a vertex model of an unsigned embedded graph. In the process of deriving this result, we show that for every diagram of a link in the 3-sphere there exists a diagram of an alternating link in a thickened surface (and an alternating virtual link) with the same Kauffman bracket. We also recover two recent results in the literature relating the Jones and Bollobas-Riordan polynomials and show they arise from two different interpretations of the same embedded graph.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-04-28T22:19:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "jones polynomial",
      "unsigned state models",
      "embedded graph",
      "vertex partition functions",
      "plane graphs"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.4152M"
    }
  }
}