{
  "id": "1404.5380",
  "version": "v1",
  "published": "2014-04-22T05:50:23.000Z",
  "updated": "2014-04-22T05:50:23.000Z",
  "title": "Lefschetz pencils and finitely presented groups",
  "authors": [
    "Ryoma Kobayashi",
    "Naoyuki Monden"
  ],
  "comment": "25 pages, 10 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "In this paper, given a finitely presented group $\\Gamma$, we provide the explicit monodromy of a Lefschetz fibration with $(-1)$-sections whose total space has fundamental group $\\Gamma$ by applying \"twisted substitutions\" to that of the Lefschetz fibration constructed by Cadavid and independently Korkmaz. Consequently, we obtain an upper bound for the minimum $g$ such that there exists a genus-$g$ Lefschetz pencil on a smooth 4-manifold whose fundamental group is isomorphic to $\\Gamma$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-22T05:50:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lefschetz pencil",
      "fundamental group",
      "total space",
      "explicit monodromy",
      "upper bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.5380K"
    }
  }
}