{
  "id": "1501.04722",
  "version": "v1",
  "published": "2015-01-20T06:56:26.000Z",
  "updated": "2015-01-20T06:56:26.000Z",
  "title": "On homotopy $K3$ surfaces constructed by two knots and their applications",
  "authors": [
    "Masatsuna Tsuchiya"
  ],
  "comment": "18 pages, 81 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let $LHT$ be a left handed trefoil knot and $K$ be any knot. We define $M_n(K)$ to be the homology $3$-sphere which is represented by a simple link of $LHT$ and $LHT \\sharp K$ with framings $0$ and $n$ respectively. Starting with this link, we construct homotopy $K3$ and spin rational homology $K3$ surfaces containing $M_n(K)$. Then we apply the adjunction inequality to show that if $n>2g^n_s(K)-2$, $M_n(K)$ does not bound any smooth spin rational $4$-ball, and that under the same assumption the negative $n$-twisted Whitehead double of $LHT \\sharp K$ is not a slice knot, where $g^n_s(K)$ is the $n$-shake genus of $K$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-20T06:56:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R65",
      "57M25"
    ],
    "keywords": [
      "applications",
      "left handed trefoil knot",
      "smooth spin rational",
      "spin rational homology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150104722T"
    }
  }
}