{
  "id": "0906.1601",
  "version": "v1",
  "published": "2009-06-08T21:12:20.000Z",
  "updated": "2009-06-08T21:12:20.000Z",
  "title": "Roots of Dehn twists",
  "authors": [
    "Darryl McCullough",
    "Kashyap Rajeevsarathy"
  ],
  "comment": "15 pages, 6 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "D. Margalit and S. Schleimer found examples of roots of the Dehn twist about a nonseparating curve in a closed orientable surface, that is, homeomorphisms whose nth power is isotopic to the Dehn twist. Our main theorem gives elementary number-theoretic conditions that describe the values of n for which an nth root exists, given the genus of the surface. Among its applications, we show that n must be odd, that the Margalit-Schleimer roots achieve the maximum value of n among the roots for a given genus, and that for a given odd n, nth roots exist for all genera greater than (n-2)(n-1)/2. We also describe all nth roots having n greater than or equal to the genus.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-06-08T21:12:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M99"
    ],
    "keywords": [
      "dehn twist",
      "nth root",
      "elementary number-theoretic conditions",
      "margalit-schleimer roots achieve",
      "main theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.1601M"
    }
  }
}