{
  "id": "math/0611077",
  "version": "v2",
  "published": "2006-11-03T18:41:02.000Z",
  "updated": "2007-03-10T17:48:59.000Z",
  "title": "Non-smoothable four-manifolds with cyclic fundamental group",
  "authors": [
    "Stefan Friedl",
    "Ian Hambleton",
    "Paul Melvin",
    "Peter Teichner"
  ],
  "comment": "We strengthened the statement of Corollary 1.4 and deleted the remark right after Corollary 1.4",
  "categories": [
    "math.GT"
  ],
  "abstract": "In [HT], two of us constructed a closed oriented 4-dimensional manifold with fundamental group $\\Z$ that does not split off $S^1\\times S^3$. In this note we show that this 4-manifold, and various others derived from it, do not admit smooth structures. Moreover, we find an infinite family of 4-manifolds with exactly the same properties (and same intersection form on $H_2$). As a corollary, we obtain topologically slice knots that are not smoothly slice in any rational homology ball.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-03-10T17:48:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R10"
    ],
    "keywords": [
      "cyclic fundamental group",
      "non-smoothable four-manifolds",
      "admit smooth structures",
      "rational homology ball",
      "intersection form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....11077F"
    }
  }
}