{
  "id": "1804.09169",
  "version": "v1",
  "published": "2018-04-24T17:53:44.000Z",
  "updated": "2018-04-24T17:53:44.000Z",
  "title": "Gluck twists of $S^4$ are diffeomorphic to $S^4$",
  "authors": [
    "Mark C. Hughes",
    "Seungwon Kim",
    "Maggie Miller"
  ],
  "comment": "17 pages, 13 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We prove that every Gluck twist on an embedded $2$-sphere in $S^4$ is diffeomorphic to $S^4$. We accomplish this by showing that a genus-$g$ surface in $\\mathbb{C}P^2$ intersecting the standard $\\mathbb{C}P^1$ in a single positive intersection point is isotopic to $\\mathbb{C}P^1$ trivially stabilized $g$ times. These results provide answers to questions of Kirby (4.24) and Gabai, as well as a partial answer to a question of Melvin.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-24T17:53:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57Q45",
      "57M99",
      "57R40"
    ],
    "keywords": [
      "gluck twist",
      "diffeomorphic",
      "single positive intersection point",
      "partial answer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}