{
  "id": "1904.12095",
  "version": "v1",
  "published": "2019-04-27T02:55:33.000Z",
  "updated": "2019-04-27T02:55:33.000Z",
  "title": "Verified computations for closed hyperbolic 3-manifolds",
  "authors": [
    "Matthias Goerner"
  ],
  "comment": "26 pages, 11 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Extending methods first used by Casson, we show how to verify a hyperbolic structure on a finite triangulation of a closed 3-manifold using interval arithmetic methods. A key ingredient is a new theoretical result (akin to a theorem by Neumann-Zagier and Moser for ideal triangulations upon which HIKMOT is based) showing that there is a redundancy among the edge equations if the edges avoid \"gimbal lock\". We successfully test the algorithm on known examples such as the orientable closed manifolds in the Hodgson-Weeks census and the bundle census by Bell. We also tackle a previously unsolved problem and determine all knots and links with up to 14 crossings that have a hyperbolic branched double cover.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-27T02:55:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50",
      "65G40"
    ],
    "keywords": [
      "verified computations",
      "closed hyperbolic",
      "interval arithmetic methods",
      "extending methods first",
      "bundle census"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}