{
  "id": "math/0603418",
  "version": "v1",
  "published": "2006-03-17T04:12:36.000Z",
  "updated": "2006-03-17T04:12:36.000Z",
  "title": "The complement of the Bowditch space in the SL(2,C) character variety",
  "authors": [
    "Shawn Pheng Keong Ng",
    "Ser Peow Tan"
  ],
  "comment": "6 pages",
  "journal": "Osaka J. Math. Volume 44, Number 2 (2007), 247-254",
  "categories": [
    "math.GT",
    "math.CV"
  ],
  "abstract": "Let ${\\mathcal X}$ be the space of type-preserving $\\SL(2,C)$ characters of the punctured torus $T$. The Bowditch space ${\\mathcal X}_{BQ}$ is the largest open subset of ${\\mathcal X}$ on which the mapping class group acts properly discontinuously, this is characterized by two simple conditions called the $BQ$-conditions. In this note, we show that $[\\rho]$ is in the interior of the complement of ${\\mathcal X}_{BQ}$ if there exists an essential simple closed curve $X$ on $T$ such that $|{\\rm tr} \\rho(X)|<0.5$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-03-17T04:12:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50"
    ],
    "keywords": [
      "bowditch space",
      "character variety",
      "complement",
      "mapping class group acts",
      "largest open subset"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......3418P"
    }
  }
}