{
  "id": "1401.1836",
  "version": "v2",
  "published": "2014-01-08T21:32:22.000Z",
  "updated": "2015-09-23T03:21:43.000Z",
  "title": "Algebraic degrees of stretch factors in mapping class groups",
  "authors": [
    "Hyunshik Shin"
  ],
  "comment": "19 pages, 5 figures; The revision contains new proof by Coxeter theory as suggested by the referee. Final version. To appear in AGT",
  "categories": [
    "math.GT"
  ],
  "abstract": "We explicitly construct pseudo-Anosov maps on the closed surface of genus $g$ with orientable foliations whose stretch factor $\\lambda$ is a Salem number with algebraic degree $2g$. Using this result, we show that there is a pseudo-Anosov map whose stretch factor has algebraic degree $d$, for each positive even integer $d$ such that $d \\leq g$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-08T21:32:22.000Z",
      "abstract": "We explicitly construct pseudo-Anosov maps on the closed surface of genus $g$ with orientable foliations whose stretch factor $\\lambda$ has algebraic degree $2g$. Using this result, we show that there is a pseudo-Anosov map whose stretch factor has algebraic degree $d$, for each positive even integer $d$ such that $d \\leq g$. Our examples also give a new approach to a conjecture of Penner.",
      "comment": "20 pages, 10 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-09-23T03:21:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50",
      "57M15"
    ],
    "keywords": [
      "algebraic degree",
      "stretch factor",
      "mapping class groups",
      "explicitly construct pseudo-anosov maps",
      "foliations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.1836S"
    }
  }
}