{
  "id": "2401.06015",
  "version": "v1",
  "published": "2024-01-11T16:25:28.000Z",
  "updated": "2024-01-11T16:25:28.000Z",
  "title": "Complexity of equal 0-surgeries",
  "authors": [
    "Marc Kegel",
    "Nicolas Weiss"
  ],
  "comment": "13 pages, 1 figure, 5 Tables",
  "categories": [
    "math.GT"
  ],
  "abstract": "We say that two knots are friends if they share the same 0-surgery. Two friends with different sliceness status would provide a counterexample to the 4-dimensional smooth Poincar\\'e conjecture. Here we create a census of all friends with small crossing numbers c and tetrahedral complexities t, and compute their smooth 4-genera. In particular, we compute the minimum of c(K)+c(K') and of t(K)+t(K') among all friends K and K'. Along the way, we classify all 0-surgeries of knots of at most 15 crossings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-11T16:25:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K10",
      "57R65",
      "57R58",
      "57K14",
      "57K32"
    ],
    "keywords": [
      "complexity",
      "smooth poincare conjecture",
      "tetrahedral complexities",
      "sliceness status",
      "small crossing numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}