{
  "id": "2111.15658",
  "version": "v3",
  "published": "2021-11-30T18:46:01.000Z",
  "updated": "2022-11-14T23:49:19.000Z",
  "title": "Pseudo-isotopies and diffeomorphisms of 4-manifolds",
  "authors": [
    "Oliver Singh"
  ],
  "comment": "57 pages, 18 figures. v2: Additional references added for examples of diffeomorphisms of 4-manifolds which are pseudo-isotopic to the identity. v3: Updated with comments from thesis examination. Fixed typographical errors, and clarified exposition in Sections 2.4 and 8",
  "categories": [
    "math.GT"
  ],
  "abstract": "A diffeomorphism $f$ of a compact manifold $X$ is pseudo-isotopic to the identity if there is a diffeomorphism $F$ of $X\\times I$ which restricts to $f$ on $X\\times 1$, and which restricts to the identity on $X\\times 0$ and $\\partial X\\times I$. We construct examples of diffeomorphisms of 4-manifolds which are pseudo-isotopic but not isotopic to the identity. To do so, we further understanding of which elements of the \"second pseudo-isotopy obstruction\", defined by Hatcher and Wagoner, can be realised by pseudo-isotopies of 4-manifolds. We also prove that all elements of the first and second pseudo-isotopy obstructions can be realised after connected sums with copies of $S^2\\times S^2$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2022-11-14T23:49:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K40",
      "57N37",
      "57R52"
    ],
    "keywords": [
      "diffeomorphism",
      "second pseudo-isotopy obstruction",
      "compact manifold",
      "construct examples",
      "pseudo-isotopic"
    ],
    "tags": [
      "dissertation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 57,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}