{
  "id": "2405.05822",
  "version": "v2",
  "published": "2024-05-09T14:59:01.000Z",
  "updated": "2024-07-10T07:19:43.000Z",
  "title": "Diffeomorphisms of 4-manifolds from degree one graspers",
  "authors": [
    "Danica Kosanović"
  ],
  "comment": "28 pages, 19 figures. v2: Minor edits",
  "categories": [
    "math.GT"
  ],
  "abstract": "We relate degree one grasper families of embedded circles to various constructions of diffeomorphisms found in the literature -- theta clasper classes of Watanabe, barbell implantations of Budney and Gabai, and twin twists of Gay and Hartman. We use a \"parameterised surgery map\" that for a smooth 4-manifold $X$ takes loops of embeddings of $S^1$ in the manifold obtained by surgery on some 2-sphere in $X$, to the mapping class group of $X$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-07-10T07:19:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R40",
      "57R50",
      "57K40",
      "57K45",
      "57S05"
    ],
    "keywords": [
      "diffeomorphisms",
      "theta clasper classes",
      "parameterised surgery map",
      "grasper families",
      "barbell implantations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}