{
  "id": "1205.1111",
  "version": "v1",
  "published": "2012-05-05T07:35:41.000Z",
  "updated": "2012-05-05T07:35:41.000Z",
  "title": "Upper bounds for the minimal number of singular fibers in a Lefschetz fibration over the torus",
  "authors": [
    "Noriyuki Hamada"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "In this paper, we give some relations in the mapping class groups of oriented closed surfaces in the form that a product of a small number of right hand Dehn twists is equal to a single commutator. Consequently, we find upper bounds for the minimal number of singular fibers in a Lefschetz fibration over the torus.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-05T07:35:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "minimal number",
      "singular fibers",
      "lefschetz fibration",
      "upper bounds",
      "right hand dehn twists"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.1111H"
    }
  }
}