{
  "id": "1602.03209",
  "version": "v1",
  "published": "2016-02-09T22:09:34.000Z",
  "updated": "2016-02-09T22:09:34.000Z",
  "title": "The quandary of quandles: The Borel completeness of a knot invariant",
  "authors": [
    "Andrew D. Brooke-Taylor",
    "Sheila K. Miller"
  ],
  "comment": "12 pages",
  "categories": [
    "math.LO",
    "math.RA"
  ],
  "abstract": "The isomorphism type of the knot quandle introduced by Joyce is a complete invariant of tame knots. Whether two quandles are isomorphic is in practice difficult to determine; we show that this question is provably hard: isomorphism of quandles is Borel complete. The class of tame knots, however, is trivial from the perspective of Borel reducibility, suggesting that equivalence of tame knots may be reducible to a more tractable isomorphism problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-09T22:09:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20N99",
      "03E15",
      "57M27"
    ],
    "keywords": [
      "borel completeness",
      "knot invariant",
      "tame knots",
      "complete invariant",
      "isomorphism type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160203209B"
    }
  }
}