{
  "id": "2203.09433",
  "version": "v1",
  "published": "2022-03-17T16:44:56.000Z",
  "updated": "2022-03-17T16:44:56.000Z",
  "title": "Diffeotopy groups of non-compact 4-manifolds",
  "authors": [
    "Isacco Nonino"
  ],
  "comment": "19 pages, 7 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We provide information on diffeotopy groups of exotic smoothings of punctured 4-manifolds, extending previous results on diffeotopy groups of exotic $\\mathbb{R}^4$'s. In particular, we prove that for a smoothable 4-manifold $M$ and for a non-empty, discrete set of points $S \\subsetneq \\mathring{M}$, there are uncountably many distinct smoothings of $M\\smallsetminus S$ whose diffeotopy groups are uncountable. We then prove that for a smoothable 4-manifold $M$ and for a non-empty, discrete set of points $S \\subsetneq \\mathring{M}$, there exists a smoothing of $M\\smallsetminus S$ whose diffeotopy groups have similar properties as $\\mathcal{R}_U$, Freedman and Taylor's universal $\\mathbb{R}^4$. Moreover, we prove that if $M$ is non-smoothable, both results still hold under the assumption that $|S| \\ge 2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-17T16:44:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R50",
      "57S05",
      "20F38",
      "57R55",
      "57K40"
    ],
    "keywords": [
      "diffeotopy groups",
      "non-compact",
      "discrete set",
      "exotic smoothings",
      "taylors universal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}