{
  "id": "2010.13292",
  "version": "v1",
  "published": "2020-10-26T02:49:27.000Z",
  "updated": "2020-10-26T02:49:27.000Z",
  "title": "Notes on constructions of knots with the same trace",
  "authors": [
    "Keiji Tagami"
  ],
  "comment": "12 pages, 7 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "The $m$-trace of a knot is the $4$-manifold obtained from $\\mathbf{B}^4$ by attaching a $2$-handle along the knot with $m$-framing. In 2015, Abe, Jong, Luecke and Osoinach introduced a technique to construct infinitely many knots with the same $m$-trace, which is called the operation $(\\ast m)$. In this paper, we prove that their technique can be explained in terms of Gompf and Miyazaki's dualizable pattern. In addition, we show that the family of knots admitting the same $4$-surgery given by Teragaito can be explained by the operation $(\\ast m)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-26T02:49:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "constructions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}