{
  "id": "math/0703196",
  "version": "v1",
  "published": "2007-03-07T13:44:58.000Z",
  "updated": "2007-03-07T13:44:58.000Z",
  "title": "Lefschetz fibrations and an invariant of finitely presented groups",
  "authors": [
    "Mustafa Korkmaz"
  ],
  "comment": "20 pages, 8 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Every finitely presented group is the fundamental group of the total space of a Lefschetz fibration. This follows from results of Gompf and Donaldson, and was also proved by Amoros-Bogomolov-Katzarkov-Pantev. We give another proof by providing the monodromy explicitly. We then define the genus of a finitely presented group $\\Gamma$ to be the minimal genus of a Lefschetz fibration with fundamental group $\\Gamma$. We also give some estimates of the genus of certain groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-03-07T13:44:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lefschetz fibration",
      "fundamental group",
      "minimal genus",
      "total space",
      "amoros-bogomolov-katzarkov-pantev"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......3196K"
    }
  }
}