{
  "id": "2210.10089",
  "version": "v1",
  "published": "2022-10-18T18:39:32.000Z",
  "updated": "2022-10-18T18:39:32.000Z",
  "title": "Unknotting number 21 knots are slice in K3",
  "authors": [
    "Marco Marengon",
    "Stefan Mihajlović"
  ],
  "comment": "13 pages, 7 figures. Comments are welcome!",
  "categories": [
    "math.GT"
  ],
  "abstract": "We prove that all knots with unknotting number at most 21 are smoothly slice in the K3 surface. We also prove a more general statement for 4-manifolds that contain a plumbing of spheres. Our strategy is based on a flexible method to remove double points of immersed surfaces in 4-manifolds by tubing over neighbourhoods of embedded trees. As a byproduct, we recover a classical result of Norman and Suzuki that every knot is smoothly slice in $S^2 \\times S^2$ and in $\\mathbb{CP}^2 \\# \\bar{\\mathbb{CP}^2}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-18T18:39:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K10",
      "57K40",
      "57R10",
      "57R40",
      "57R42",
      "57R45"
    ],
    "keywords": [
      "unknotting number",
      "smoothly slice",
      "general statement",
      "k3 surface",
      "remove double points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}