{
  "id": "math/0109011",
  "version": "v4",
  "published": "2001-09-03T12:14:11.000Z",
  "updated": "2003-03-19T13:53:12.000Z",
  "title": "Lefschetz fibrations with unbounded Euler class",
  "authors": [
    "Thilo Kuessner"
  ],
  "comment": "8 pages, submitted to NYJM",
  "categories": [
    "math.GT",
    "math.AT",
    "math.SG"
  ],
  "abstract": "We investigate the bounded cohomology of Lefschetz fibrations. If a Lefschetz fibration has regular fiber of genus at least 2 and it has at least two distinct vanishing cycles, we show that its Euler class is not bounded. As a consequence, we exclude the existence of negatively curved metrics on Lefschetz fibrations with more than one singular fiber.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2003-03-19T13:53:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57N65"
    ],
    "keywords": [
      "lefschetz fibration",
      "unbounded euler class",
      "singular fiber",
      "distinct vanishing cycles",
      "regular fiber"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......9011K"
    }
  }
}