{
  "id": "1705.09854",
  "version": "v1",
  "published": "2017-05-27T18:56:36.000Z",
  "updated": "2017-05-27T18:56:36.000Z",
  "title": "Trisections of 4-manifolds via Lefschetz fibrations",
  "authors": [
    "Nickolas A. Castro",
    "Burak Ozbagci"
  ],
  "comment": "23 pages, 10 figures",
  "categories": [
    "math.GT",
    "math.SG"
  ],
  "abstract": "We use Lefschetz fibrations to give an alternate proof of a recent result of Gay and Kirby which says that every smooth, closed, oriented, connected 4-manifold admits a trisection. The key feature of our proof is that contact geometry plays a crucial role instead of Cerf theory. As an application, we describe an explicit trisection diagram of a closed 4-manifold which admits a Lefschetz fibration over the 2-sphere equipped with a section of square -1, based only on the vanishing cycles of the Lefschetz fibration.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-27T18:56:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lefschetz fibration",
      "contact geometry plays",
      "explicit trisection diagram",
      "cerf theory",
      "alternate proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}