{
  "id": "1602.02584",
  "version": "v1",
  "published": "2016-02-08T14:34:03.000Z",
  "updated": "2016-02-08T14:34:03.000Z",
  "title": "$C_{n}$-moves and the difference of Jones polynomials for links",
  "authors": [
    "Ryo Nikkuni"
  ],
  "comment": "13 pages, 11 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "The Jones polynomial $V_{L}(t)$ for an oriented link $L$ is a one-variable Laurent polynomial link invariant discovered by Jones. For any integer $n\\ge 3$, we show that: (1) the difference of Jones polynomials for two oriented links which are $C_{n}$-equivalent is divisible by $\\left(t-1\\right)^{n}\\left(t^{2}+t+1\\right)\\left(t^{2}+1\\right)$, and (2) there exists a pair of two oriented knots which are $C_{n}$-equivalent such that the difference of the Jones polynomials for them equals $\\left(t-1\\right)^{n}\\left(t^{2}+t+1\\right)\\left(t^{2}+1\\right)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-08T14:34:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25"
    ],
    "keywords": [
      "jones polynomial",
      "difference",
      "one-variable laurent polynomial link invariant",
      "oriented link",
      "equivalent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160202584N"
    }
  }
}