{
  "id": "math/0412074",
  "version": "v1",
  "published": "2004-12-03T13:47:26.000Z",
  "updated": "2004-12-03T13:47:26.000Z",
  "title": "Span of the Jones polynomial of an alternating virtual link",
  "authors": [
    "Naoko Kamada"
  ],
  "comment": "Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-46.abs.html",
  "journal": "Algebr. Geom. Topol. 4 (2004) 1083-1101",
  "categories": [
    "math.GT"
  ],
  "abstract": "For an oriented virtual link, L.H. Kauffman defined the f-polynomial (Jones polynomial). The supporting genus of a virtual link diagram is the minimal genus of a surface in which the diagram can be embedded. In this paper we show that the span of the f-polynomial of an alternating virtual link L is determined by the number of crossings of any alternating diagram of L and the supporting genus of the diagram. It is a generalization of Kauffman-Murasugi-Thistlethwaite's theorem. We also prove a similar result for a virtual link diagram that is obtained from an alternating virtual link diagram by virtualizing one real crossing. As a consequence, such a diagram is not equivalent to a classical link diagram.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-12-03T13:47:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "jones polynomial",
      "supporting genus",
      "alternating virtual link diagram",
      "similar result",
      "f-polynomial"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}