{
  "id": "1609.07289",
  "version": "v1",
  "published": "2016-09-23T09:40:13.000Z",
  "updated": "2016-09-23T09:40:13.000Z",
  "title": "The $\\mathfrak{sl}_3$ colored Jones polynomials for $2$-bridge links",
  "authors": [
    "Wataru Yuasa"
  ],
  "comment": "28 pages, many TikZ pictures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Kuperberg introduced web spaces for some Lie algebras which are generalizations of the Kauffman bracket skein module on a disk with marked points. We derive some formulas for $A_1$ and $A_2$ clasped web spaces by graphical calculus using skein theory. These formulas are colored version of skein relations, twist formulas and bubble skein expansion formulas. We calculate the $\\mathfrak{sl}_2$ and $\\mathfrak{sl}_3$ colored Jones polynomials of $2$-bridge knots and links explicitly using twist formulas.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-23T09:40:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "colored jones polynomials",
      "bridge links",
      "kauffman bracket skein module",
      "twist formulas",
      "bubble skein expansion formulas"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}