{
  "id": "2107.03275",
  "version": "v1",
  "published": "2021-07-07T15:09:50.000Z",
  "updated": "2021-07-07T15:09:50.000Z",
  "title": "Euclidean volumes of hyperbolic knots",
  "authors": [
    "Nikolay Abrosimov",
    "Alexander Kolpakov",
    "Alexander Mednykh"
  ],
  "comment": "11 pages, 2 figures",
  "categories": [
    "math.GT",
    "math.NT"
  ],
  "abstract": "The hyperbolic structure on a 3-dimensional cone-manifold with a knot as singularity can often be deformed into a limiting Euclidean structure. In the present paper we show that the respective normalised Euclidean volume is always an algebraic number. This stands in contrast to hyperbolic volumes whose number-theoretic nature is usually quite complicated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-07T15:09:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K10",
      "57M50",
      "11R04"
    ],
    "keywords": [
      "hyperbolic knots",
      "respective normalised euclidean volume",
      "hyperbolic volumes",
      "algebraic number",
      "limiting euclidean structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}