{
  "id": "1601.01985",
  "version": "v1",
  "published": "2016-01-08T19:28:45.000Z",
  "updated": "2016-01-08T19:28:45.000Z",
  "title": "Non-characterizing slopes for hyperbolic knots",
  "authors": [
    "Kenneth L. Baker",
    "Kimihiko Motegi"
  ],
  "comment": "13 pages, 7 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "A non-trivial slope $r$ on a knot $K$ in $S^3$ is called a characterizing slope if whenever the result of $r$-surgery on a knot $K'$ is orientation preservingly homeomorphic to the result of $r$-surgery on $K$, then $K'$ is isotopic to $K$. Ni and Zhang ask: for any hyperbolic knot $K$, is a slope $r = p/q$ with $|p| + |q|$ sufficiently large a characterizing slope? In this article we answer this question in the negative by demonstrating that there is a hyperbolic knot $K$ in $S^3$ which has infinitely many non-characterizing slopes. As the simplest known example, the hyperbolic knot $8_6$ has no integral characterizing slopes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-08T19:28:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25"
    ],
    "keywords": [
      "hyperbolic knot",
      "non-characterizing slopes",
      "zhang ask",
      "integral characterizing slopes",
      "non-trivial slope"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160101985B"
    }
  }
}