{
  "id": "1208.1559",
  "version": "v4",
  "published": "2012-08-08T01:21:09.000Z",
  "updated": "2015-09-01T16:04:03.000Z",
  "title": "Essential open book foliation and fractional Dehn twist coefficient",
  "authors": [
    "Tetsuya Ito",
    "Keiko Kawamuro"
  ],
  "comment": "58 pages, 35 figures",
  "categories": [
    "math.GT",
    "math.SG"
  ],
  "abstract": "We introduce an essential open book foliation, a refinement of the open book foliation, and develop technical estimates of the fractional Dehn twist coefficient (FDTC) of monodromies and the FDTC for closed braids, which we introduce as well. As applications, we quantitatively study the `gap' of overtwisted contact structures and a non-right-veering monodromies. We give sufficient conditions for a 3-manifold to be irreducible and atoroidal. We also show that the geometries of a 3-manifold and the complement of a closed braid are determined by the Nielsen-Thurston types of the monodromies of their open book decompositions.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-12-27T21:23:13.000Z",
      "comment": "41 pages, 19 figures. Title and abstract are changed. The main result (Theorem 8.3) is much stronger than the original one. A number of new results (Theorems 7.8, 7.12 Corollary 7.13, Theorem 8.14 etc.) are added",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2015-09-01T16:04:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50",
      "53D35",
      "57R17"
    ],
    "keywords": [
      "essential open book foliation",
      "fractional dehn twist coefficient",
      "open book decompositions",
      "closed braid",
      "monodromies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 58,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.1559I"
    }
  }
}