{
  "id": "0712.1583",
  "version": "v2",
  "published": "2007-12-10T20:31:04.000Z",
  "updated": "2008-06-04T06:36:30.000Z",
  "title": "On fibering and splitting of 5-manifolds over the circle",
  "authors": [
    "Qayum Khan"
  ],
  "comment": "22 pages, exposition revised for better self-containment",
  "journal": "Topology and its Applications, Volume 156, Number 2 (2008), 284--299",
  "doi": "10.1016/j.topol.2008.07.007",
  "categories": [
    "math.GT",
    "math.AT"
  ],
  "abstract": "Our main result is a generalization of Cappell's 5-dimensional splitting theorem. As an application, we analyze, up to internal s-cobordism, the smoothable splitting and fibering problems for certain 5-manifolds mapping to the circle. For example, these maps may have homotopy fibers which are in the class of finite connected sums of certain geometric 4-manifolds. Most of these homotopy fibers have non-vanishing second mod 2 homology and have fundamental groups of exponential growth, which are not known to be tractable by Freedman--Quinn topological surgery. Indeed, our key technique is topological cobordism, which may not be the trace of surgeries.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-06-04T06:36:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "homotopy fibers",
      "main result",
      "freedman-quinn topological surgery",
      "exponential growth",
      "fundamental groups"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0712.1583K"
    }
  }
}