{
  "id": "1810.11773",
  "version": "v1",
  "published": "2018-10-28T07:26:12.000Z",
  "updated": "2018-10-28T07:26:12.000Z",
  "title": "On The Jones Polynomial of Quasi-alternating Links",
  "authors": [
    "Nafaa Chbili",
    "Khaled Qazaqzeh"
  ],
  "comment": "11 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "We prove that twisting any quasi-alternating link $L$ with no gaps in its Jones polynomial $V_L(t)$ at the crossing where it is quasi-alternating produces a link $L^{*}$ with no gaps in its Jones polynomial $V_{L^*}(t)$. This leads us to conjecture that the Jones polynomial of any prime quasi-alternating link, other than $(2,n)$-torus links, has no gaps. This would give a new property of quasi-alternating links and a simple obstruction criterion for a link to be quasi-alternating. We prove that the conjecture holds for quasi-alternating Montesinos links as well as quasi-alternating links with braid index 3.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-28T07:26:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25"
    ],
    "keywords": [
      "jones polynomial",
      "simple obstruction criterion",
      "braid index",
      "prime quasi-alternating link",
      "conjecture holds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}