{
  "id": "math/0509033",
  "version": "v1",
  "published": "2005-09-02T08:47:27.000Z",
  "updated": "2005-09-02T08:47:27.000Z",
  "title": "The SL(2,C) character variety of the one-holed torus",
  "authors": [
    "Ser Peow Tan",
    "Yan Loi Wong",
    "Ying Zhang"
  ],
  "comment": "8 pages, announcement",
  "journal": "Electron. Res. Announc. Amer. Math. Soc. 11 (2005) 103-110",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "In this note we announce several results concerning the SL(2,C) character variety ${\\mathcal X}$ of the one-holed torus. We give a description of the largest open subset ${\\mathcal X}_{BQ}$ of ${\\mathcal X}$ on which the mapping class group $\\Gamma$ acts properly discontinuously, in terms of two very simple conditions, and show that a series identity generalizing McShane's identity for the punctured torus holds for all characters in this subset. We also give variations of the McShane-Bowditch identities to characters fixed by an Anosov element of $\\Gamma$ with applications to closed hyperbolic three manifolds. Finally we give a definition of end invariants for SL(2,C) characters and give a partial classification of the set of end invariants of a character in ${\\mathcal X}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-09-02T08:47:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32G15",
      "57M50",
      "30F60"
    ],
    "keywords": [
      "character variety",
      "one-holed torus",
      "series identity generalizing mcshanes identity",
      "end invariants",
      "largest open subset"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Electron. Res. Announc. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......9033P"
    }
  }
}