{
  "id": "2003.07163",
  "version": "v1",
  "published": "2020-03-16T12:52:55.000Z",
  "updated": "2020-03-16T12:52:55.000Z",
  "title": "Knots with infinitely many non-characterizing slopes",
  "authors": [
    "Tetsuya Abe",
    "Keiji Tagami"
  ],
  "comment": "21 pages, 21 figures. Comments are welcome!",
  "categories": [
    "math.GT"
  ],
  "abstract": "Using the techniques on annulus twists, we observe that $6_3$ has infinitely many non-characterizing slopes, which affirmatively answers a question by Baker and Motegi. Furthermore, we prove that the knots $6_2$, $6_3$, $7_6$, $7_7$, $8_1$, $8_3$, $8_4$, $8_6$, $8_7$, $8_9$, $8_{10}$, $8_{11}$, $8_{12}$, $8_{13}$, $8_{14}$, $8_{17}$,$8_{20}$ and $8_{21}$ have infinitely many non-characterizing slopes. We also introduce the notion of trivial annulus twists and give some possible applications. Finally, we completely determine which knots have special annulus presentations up to 8-crossings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-16T12:52:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25"
    ],
    "keywords": [
      "non-characterizing slopes",
      "trivial annulus twists",
      "special annulus presentations",
      "techniques",
      "affirmatively answers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}