{
  "id": "math/0404475",
  "version": "v2",
  "published": "2004-04-27T01:36:17.000Z",
  "updated": "2004-06-02T21:03:08.000Z",
  "title": "The Kauffman bracket and the Bollobas-Riordan polynomial of ribbon graphs",
  "authors": [
    "Sergei Chmutov",
    "Igor Pak"
  ],
  "comment": "Some references added",
  "categories": [
    "math.GT",
    "math.CO"
  ],
  "abstract": "For a ribbon graph $G$ we consider an alternating link $L_G$ in the 3-manifold $G\\times I$ represented as the product of the oriented surface $G$ and the unit interval $I$. We show that the Kauffman bracket $[L_G]$ is an evaluation of the recently introduced Bollobas-Riordan polynomial $R_G$. This results generalizes the celebrated relation between Kauffman bracket and Tutte polynomial of planar graphs.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-06-02T21:03:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M15",
      "57M25",
      "05C10",
      "05C15"
    ],
    "keywords": [
      "kauffman bracket",
      "bollobas-riordan polynomial",
      "ribbon graph",
      "tutte polynomial",
      "results generalizes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......4475C"
    }
  }
}