{
  "id": "1404.5119",
  "version": "v2",
  "published": "2014-04-21T06:06:43.000Z",
  "updated": "2014-05-08T15:32:11.000Z",
  "title": "Trivalent graphs, volume conjectures and character varieties",
  "authors": [
    "Satoshi Nawata",
    "P. Ramadevi",
    "Zodinmawia"
  ],
  "comment": "11 pages, 2 figures",
  "categories": [
    "math.GT",
    "hep-th",
    "math-ph",
    "math.MP",
    "math.QA"
  ],
  "abstract": "The generalized volume conjecture and the AJ conjecture (a.k.a. the quantum volume conjecture) are extended to $U_q(\\fraksl_2)$ colored quantum invariants of the theta and tetrahedron graph. The $\\SL(2,\\bC)$ character variety of the fundamental group of the complement of a trivalent graph with $E$ edges in $S^3$ is a Lagrangian subvariety of the Hitchin moduli space over the Riemann surface of genus $g=E/3+1$. For the theta and tetrahedron graph, we conjecture that the configuration of the character variety is locally determined by large color asymptotics of the quantum invariants of the trivalent graph in terms of complex Fenchel-Nielsen coordinates. Moreover, the $q$-holonomic difference equation of the quantum invariants provides the quantization of the character variety.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-05-08T15:32:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "character variety",
      "trivalent graph",
      "quantum invariants",
      "tetrahedron graph",
      "quantum volume conjecture"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s11005-014-0713-2",
      "journal": "Letters in Mathematical Physics",
      "year": 2014,
      "month": "Oct",
      "volume": 104,
      "number": 10,
      "pages": 1303
    },
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1291389,
      "adsabs": "2014LMaPh.104.1303N"
    }
  }
}