{
  "id": "1101.2383",
  "version": "v2",
  "published": "2011-01-12T15:16:20.000Z",
  "updated": "2011-04-14T18:55:34.000Z",
  "title": "On pseudo-Anosov mapping classes with minimum dilatation and Lanneau-Thiffeault numbers",
  "authors": [
    "Joan S. Birman"
  ],
  "comment": "Lemma 3 of version 1 is false. All other changes are minor, and were directed toward making the paper readable without the false lemma. new version has 14 pages, 4 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "It has been known since 1981 that if one fixes an orientable surface $S$ of genus $g$, then there is a real number $\\lambda_{min,g} > 1$ that is the dilatation of a pA diffeomorphism of $S$, and every other pA diffeomorphism of $S$ has dilatation $\\geq \\lambda_{min,g}$. We will show how a little-known theorem about digraphs gives some insight into $\\lambda_{min,g}$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-04-14T18:55:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "pseudo-anosov mapping classes",
      "minimum dilatation",
      "lanneau-thiffeault numbers",
      "pa diffeomorphism",
      "real number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1101.2383B"
    }
  }
}