{
  "id": "1705.09989",
  "version": "v1",
  "published": "2017-05-28T20:45:35.000Z",
  "updated": "2017-05-28T20:45:35.000Z",
  "title": "The 4-Dimensional Light Bulb Theorem",
  "authors": [
    "David Gabai"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "For embedded 2-spheres in a 4-manifold sharing the same embedded transverse sphere homotopy implies isotopy, provided the ambient 4-manifold has no $\\mathbb Z_2$-torsion in the fundamental group. Among other things, this leads to a generalization of the classical light bulb trick to 4-dimensions, the uniqueness of spanning discs for simple closed curves in $S^4$ and $\\pi_0(\\textrm{Diff}_0(S^2\\times D^2)/\\textrm{Diff}_0(B^4))=1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-28T20:45:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57N13",
      "57N35"
    ],
    "keywords": [
      "light bulb theorem",
      "transverse sphere homotopy implies isotopy",
      "embedded transverse sphere homotopy implies",
      "classical light bulb trick",
      "fundamental group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}