{
  "id": "2306.06533",
  "version": "v1",
  "published": "2023-06-10T22:00:21.000Z",
  "updated": "2023-06-10T22:00:21.000Z",
  "title": "$n$-knots in $S^n\\times S^2$ and contractible $(n+3)$-manifolds",
  "authors": [
    "Geunyoung Kim"
  ],
  "comment": "14 pages, 8 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "In $1961$, Mazur constructed a contractible, compact, smooth $4$-manifold with boundary which is not homeomorphic to the standard $4$-ball, using a $0$-handle, a $1$-handle and a $2$-handle. In this paper, for any integer $n\\geq2,$ we construct a contractible, compact, smooth $(n+3)$-manifold with boundary which is not homeomorphic to the standard $(n+3)$-ball, using a $0$-handle, an $n$-handle and an $(n+1)$-handle. The key step is the construction of an interesting knotted $n$-sphere in $S^n\\times S^2$ generalizing the Mazur pattern.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-10T22:00:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K45",
      "57K50",
      "57R65"
    ],
    "keywords": [
      "contractible",
      "homeomorphic",
      "construction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}