{
  "id": "0805.1447",
  "version": "v2",
  "published": "2008-05-10T09:52:14.000Z",
  "updated": "2008-10-22T13:37:24.000Z",
  "title": "Braid ordering and the geometry of closed braid",
  "authors": [
    "Tetsuya Ito"
  ],
  "comment": "21 pages, 10 figures: Some figures are rewritten. Especially mistaken figure 2 is corrected",
  "journal": "Geom. Topol. 15 (2011) 473-498",
  "doi": "10.2140/gt.2011.15.473",
  "categories": [
    "math.GT"
  ],
  "abstract": "The relationships between braid ordering and the geometry of its closure is studied. We prove that if an essential closed surface $F$ in the complements of closed braid has relatively small genus with respect to the Dehornoy floor of the braid, $F$ is circular-foliated in a sense of Birman-Menasco's Braid foliation theory. As an application of the result, we prove that if Dehornoy floor of braids are larger than three, Nielsen-Thurston classification of braids and the geometry of their closure's complements are in one-to-one correspondence. Using this result, we construct infinitely many hyperbolic knots explicitly from pseudo-Anosov element of mapping class groups.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-10-22T13:37:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25"
    ],
    "keywords": [
      "closed braid",
      "braid ordering",
      "dehornoy floor",
      "birman-menascos braid foliation theory",
      "pseudo-anosov element"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0805.1447I"
    }
  }
}