{
  "id": "0711.3490",
  "version": "v3",
  "published": "2007-11-22T00:00:10.000Z",
  "updated": "2008-12-16T14:59:24.000Z",
  "title": "Generalized duality for graphs on surfaces and the signed Bollobas-Riordan polynomial",
  "authors": [
    "Sergei Chmutov"
  ],
  "comment": "To appear in J. Combin. Theory Ser. B (2009), doi:10.1016/j.jctb.2008.09.007",
  "categories": [
    "math.CO",
    "math.GT"
  ],
  "abstract": "We generalize the natural duality of graphs embedded into a surface to a duality with respect to a subset of edges. The dual graph might be embedded into a different surface. We prove a relation between the signed Bollobas-Riordan polynomials of dual graphs. This relation unifies various recent results expressing the Jones polynomial of links as specializations of the Bollobas-Riordan polynomials.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-12-16T14:59:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C10",
      "57M15",
      "57M27"
    ],
    "keywords": [
      "signed bollobas-riordan polynomial",
      "generalized duality",
      "dual graph",
      "jones polynomial",
      "relation unifies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.3490C"
    }
  }
}