{
  "id": "2206.11243",
  "version": "v1",
  "published": "2022-06-22T17:44:31.000Z",
  "updated": "2022-06-22T17:44:31.000Z",
  "title": "Unknotting 3-balls in the 5-ball",
  "authors": [
    "Daniel Hartman"
  ],
  "comment": "6 pages, 3 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "The purpose of this note is to answer affirmatively a question posed by both Gay, and Hughes, Kim and Miller as to whether every $3$--ball smoothly embedded in the $4$--sphere becomes isotopic relative to the bounding 2-sphere when pushed into the 5-ball. In fact, we show that any two collections of disjointly embedded smooth $3$--balls bounding an unlink of 2--spheres in $S^4$ are isotopic relative to the unlink when pushed into the $5$--ball.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-22T17:44:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R52",
      "57K45"
    ],
    "keywords": [
      "unknotting",
      "isotopic relative",
      "collections",
      "disjointly embedded smooth"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}