{
  "id": "1508.01491",
  "version": "v1",
  "published": "2015-08-06T19:01:56.000Z",
  "updated": "2015-08-06T19:01:56.000Z",
  "title": "Nonexistence of Stein structures on 4-manifolds and maximal Thurston-Bennequin numbers",
  "authors": [
    "Kouichi Yasui"
  ],
  "comment": "10 pages, 10 figures",
  "categories": [
    "math.GT",
    "math.SG"
  ],
  "abstract": "For a 4-manifold represented by a framed knot in $S^3$, it has been well known that the 4-manifold admits a Stein structure if the framing is less than the maximal Thurston-Bennequin number of the knot. In this paper we prove either the converse of this fact is false or there exists a compact contractible oriented smooth 4-manifold admitting no Stein structure. Note that an exotic smooth structure on $S^4$ exists if and only if there exists a compact contractible oriented smooth 4-manifold with $S^3$ boundary admitting no Stein structure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-06T19:01:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R55",
      "57R65",
      "57R17",
      "57M25"
    ],
    "keywords": [
      "maximal thurston-bennequin number",
      "stein structure",
      "compact contractible oriented smooth",
      "nonexistence",
      "exotic smooth structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150801491Y"
    }
  }
}