{
  "id": "1612.03368",
  "version": "v1",
  "published": "2016-12-11T02:57:02.000Z",
  "updated": "2016-12-11T02:57:02.000Z",
  "title": "On the question of genericity of hyperbolic knots",
  "authors": [
    "Andrei Malyutin"
  ],
  "comment": "22 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "A well-known conjecture in knot theory says that the percentage of hyperbolic knots amongst all of the prime knots of $n$ or fewer crossings approaches $100$ as $n$ approaches infinity. In this paper, it is proved that this conjecture contradicts several other plausible conjectures, including the 120-year-old conjecture on additivity of the crossing number of knots under connected sum and the conjecture that the crossing number of a satellite knot is not less than that of its companion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-11T02:57:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "60G50",
      "20F65",
      "20F67",
      "20F36"
    ],
    "keywords": [
      "hyperbolic knots",
      "genericity",
      "crossing number",
      "fewer crossings approaches",
      "knot theory says"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}