{
  "id": "1908.06187",
  "version": "v1",
  "published": "2019-08-16T21:46:08.000Z",
  "updated": "2019-08-16T21:46:08.000Z",
  "title": "Hyperbolic knots are not generic",
  "authors": [
    "Yury Belousov",
    "Andrei Malyutin"
  ],
  "comment": "Preliminary version, 4 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "We show that the proportion of hyperbolic knots among all of the prime knots of $n$ or fewer crossings does not converge to $1$ as $n$ approaches infinity. Moreover, we show that if $K$ is a nontrivial knot then the proportion of satellites of $K$ among all of the prime knots of $n$ or fewer crossings does not converge to $0$ as $n$ approaches infinity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-16T21:46:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25"
    ],
    "keywords": [
      "hyperbolic knots",
      "prime knots",
      "fewer crossings",
      "approaches infinity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}