{
  "id": "math/9812051",
  "version": "v3",
  "published": "1998-12-08T22:02:38.000Z",
  "updated": "1999-02-22T19:37:09.000Z",
  "title": "Minimal number of singular fibers in a Lefschetz fibration",
  "authors": [
    "Mustafa Korkmaz",
    "Burak Ozbagci"
  ],
  "comment": "6 pages, 2 figures, second version",
  "journal": "Proc. Amer. Math. Soc. 129 (2001), 1545-1549",
  "categories": [
    "math.GT",
    "math.SG"
  ],
  "abstract": "There exists a (relatively minimal) genus g Lefschetz fibration with only one singular fiber over a closed (Riemann) surface of genus h iff g>2 and h>1. The singular fiber can be chosen to be reducible or irreducible. Other results are that every Dehn twist on a closed surface of genus at least three is a product of two commutators and no Dehn twist on any closed surface is equal to a single commutator.",
  "revisions": [
    {
      "version": "v3",
      "updated": "1999-02-22T19:37:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M99",
      "20F38"
    ],
    "keywords": [
      "singular fiber",
      "lefschetz fibration",
      "minimal number",
      "dehn twist",
      "closed surface"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Proc. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math.....12051K"
    }
  }
}