{
  "id": "2412.01648",
  "version": "v1",
  "published": "2024-12-02T15:58:48.000Z",
  "updated": "2024-12-02T15:58:48.000Z",
  "title": "Minimum dilatations of pseudo-Anosov braids",
  "authors": [
    "Chi Cheuk Tsang",
    "Xiangzhuo Zeng"
  ],
  "comment": "82 pages, 13 figures",
  "categories": [
    "math.GT",
    "math.DS"
  ],
  "abstract": "We determine the minimum dilatation $\\delta_n$ among pseudo-Anosov braids with $n$ strands, for large enough values of $n$. This confirms a conjecture of Venzke that $\\lim_{n \\to \\infty} \\delta_n^n = (2+\\sqrt{3})^2 \\approx 13.928$. Together with previous work, this also solves the minimum dilatation problem on the $n$-punctured sphere, for all but $6$ values of $n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-12-02T15:58:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "pseudo-anosov braids",
      "minimum dilatation problem",
      "conjecture",
      "punctured sphere"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 82,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}