{
  "id": "1807.11453",
  "version": "v1",
  "published": "2018-07-30T17:22:01.000Z",
  "updated": "2018-07-30T17:22:01.000Z",
  "title": "Geometrically simply connected 4-manifolds and stable cohomotopy Seiberg-Witten invariants",
  "authors": [
    "Kouichi Yasui"
  ],
  "comment": "7 pages",
  "categories": [
    "math.GT",
    "math.SG"
  ],
  "abstract": "We show that every positive definite closed oriented 4-manifold with $b_2^+>1$ and without 1-handles has a vanishing stable cohomotopy Seiberg-Witten invariant, and thus admits no symplectic structure. We also show that every closed oriented 4-manifold with $b_2^+\\equiv b_2^-\\equiv 3\\pmod{4}$ and without 1-handles admits no symplectic structure for at least one orientation of the manifold. In fact, we prove these results for non-simply connected 4-manifolds as well, by relaxing the condition `without 1-handles'.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-30T17:22:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R55",
      "57R65",
      "57R17"
    ],
    "keywords": [
      "symplectic structure",
      "vanishing stable cohomotopy seiberg-witten invariant",
      "orientation",
      "positive definite"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}