{
  "id": "math/0302026",
  "version": "v3",
  "published": "2003-02-03T17:02:21.000Z",
  "updated": "2003-10-21T21:14:07.000Z",
  "title": "Four-manifolds of large negative deficiency",
  "authors": [
    "Charles Livingston"
  ],
  "comment": "9 pages, references added, minor corrections and simplified proof of main theorem",
  "journal": "Math. Proc. Camb. 138 (2005) 107-115.",
  "categories": [
    "math.GT"
  ],
  "abstract": "For every N > 0 there exists a group of deficiency less than -N that arises as the fundamental group of a smooth homology 4-sphere and also as the fundamental group of the complement of a compact contractible submanifold of the 4-sphere. A group is the fundamental group of the complement of a contractible submanifold of the n-sphere, n > 4, if and only if it is the fundamental group of a homology n-sphere. There exist fundamental groups of homology n-spheres, n > 4, that cannot arise as the fundamental group of the complement of a contractible submanifold of the 4-sphere.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2003-10-21T21:14:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57N65",
      "57M05",
      "57Q45"
    ],
    "keywords": [
      "fundamental group",
      "large negative deficiency",
      "homology n-sphere",
      "four-manifolds",
      "complement"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......2026L"
    }
  }
}