{
  "id": "1610.04033",
  "version": "v1",
  "published": "2016-10-13T11:27:12.000Z",
  "updated": "2016-10-13T11:27:12.000Z",
  "title": "Nonexistence of twists generating exotic 4-manifolds",
  "authors": [
    "Kouichi Yasui"
  ],
  "comment": "10 pages, no figures",
  "categories": [
    "math.GT",
    "math.SG"
  ],
  "abstract": "It is well known that, for any exotic pair of simply connected closed 4-manifolds, one is obtained by twisting the other along a contractible submanifold. In contrast to this fact, we show that there exists an infinite family of pairwise exotic 4-manifolds such that, for any 4-manifold $X$ and any compact codimension zero submanifold $W$ with $b_1(\\partial W)=0$, the family cannot be generated by twisting $X$ along $W$ and varying the gluing map. Furthermore, for any member $X$ and any submanifold $W$ with a certain mild condition, the family cannot be generated from $X$ by removing $W$ and gluing other 4-manifolds. We moreover provide various such families.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-13T11:27:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R55",
      "57R65",
      "57R17"
    ],
    "keywords": [
      "twists generating exotic",
      "nonexistence",
      "compact codimension zero submanifold",
      "mild condition",
      "exotic pair"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}