{
  "id": "1704.04419",
  "version": "v1",
  "published": "2017-04-14T13:33:51.000Z",
  "updated": "2017-04-14T13:33:51.000Z",
  "title": "On intersection forms of definite 4-manifolds bounded by a rational homology 3-sphere",
  "authors": [
    "Dong Heon Choe",
    "Kyungbae Park"
  ],
  "comment": "16 pages, 4 figures",
  "categories": [
    "math.GT",
    "math.NT"
  ],
  "abstract": "We show that, if a rational homology 3-sphere $Y$ bounds a positive definite smooth 4-manifold, then there are finitely many negative definite lattices, up to the stable-equivalence, which can be realized as the intersection form of a smooth 4-manifold bounded by $Y$. To this end, we make use of constraints on definite forms bounded by $Y$ induced from Donaldson's diagonalization theorem, and Ozsv\\'ath and Szab\\'o's Heegaard Floer correction term. We also present some families of Seifert fibered 3-manifolds that bound both positive and negative definite smooth 4-manifolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-14T13:33:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rational homology",
      "intersection form",
      "szabos heegaard floer correction term",
      "donaldsons diagonalization theorem",
      "negative definite smooth"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}