{
  "id": "2003.03925",
  "version": "v1",
  "published": "2020-03-09T05:19:15.000Z",
  "updated": "2020-03-09T05:19:15.000Z",
  "title": "Isotopy of the Dehn twist on K3#K3 after a single stablization",
  "authors": [
    "Jianfeng Lin"
  ],
  "categories": [
    "math.GT",
    "math.AT"
  ],
  "abstract": "Kronheimer-Mrowka recently proved that the Dehn twist along a 3-sphere in the neck of $K3\\#K3$ is not smoothly isotopic to the identity. This provides a new example of self-diffeomorphisms on 4-manifolds that are isotopic to the identity in the topological category but not smoothly so. (The first such examples were given by Ruberman.) In this paper, we use the Pin(2)-equivariant Bauer-Furuta invariant to show that this Dehn twist is not smoothly isotopic to the identity even after a single stabilization (connected summing with the identity map on $S^{2}\\times S^{2}$). This gives the first example of exotic phenomenon in dimension 4 that does not disappear after a single stabilization.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-09T05:19:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R57",
      "57R50",
      "57R52",
      "55P91"
    ],
    "keywords": [
      "dehn twist",
      "single stablization",
      "single stabilization",
      "smoothly isotopic",
      "identity map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}