{
  "id": "1501.01128",
  "version": "v1",
  "published": "2015-01-06T10:23:12.000Z",
  "updated": "2015-01-06T10:23:12.000Z",
  "title": "S-Cobordism Classification of $4$-Manifolds Through the Group of Homotopy Self-Equivalences",
  "authors": [
    "Friedrich Hegenbarth",
    "Mehmetcik Pamuk",
    "Dušan Repovš"
  ],
  "comment": "appears in Mediterr. J. Math. (2015)",
  "doi": "10.1007/s00009-014-0456-4",
  "categories": [
    "math.GT",
    "math.AT"
  ],
  "abstract": "The aim of this paper is to give an $s$-cobordism classification of topological $4$-manifolds in terms of the standard invariants using the group of homotopy self-equivalences. Hambleton and Kreck constructed a braid to study the group of homotopy self-equivalences of $4$-manifolds. Using this braid together with the modified surgery theory of Kreck, we give an $s$-cobordism classification for certain $4$-manifolds with fundamental group $\\pi$, such that cd $\\pi \\leq 2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-06T10:23:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57N13",
      "55P10",
      "57R80"
    ],
    "keywords": [
      "homotopy self-equivalences",
      "s-cobordism classification",
      "standard invariants",
      "modified surgery theory",
      "fundamental group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150101128H"
    }
  }
}