{
  "id": "1906.08723",
  "version": "v1",
  "published": "2019-06-20T16:08:15.000Z",
  "updated": "2019-06-20T16:08:15.000Z",
  "title": "Problem on Mutant Pairs of Hyperbolic Polyhedra",
  "authors": [
    "Croix Gyurek",
    "Roland Roeder"
  ],
  "comment": "8 pages, 3 figures, and several explicit examples. This is an open problems paper. Comments are welcome!",
  "categories": [
    "math.GT"
  ],
  "abstract": "We present a notion of mutation of hyperbolic polyhedra, analogous to mutation in knot theory, and then present a general question about commensurability of mutant pairs of polyhedra. We motivate that question with several concrete examples of mutant pairs for which commensurability is unknown. The polyhedra we consider are compact, so techniques involving cusps that are typically used to distinguishing mutant pairs of knots are not applicable. Indeed, new techniques may need to be developed to study commensurability of mutant pairs of polyhedra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-20T16:08:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30F40",
      "52B10",
      "51M09"
    ],
    "keywords": [
      "hyperbolic polyhedra",
      "knot theory",
      "techniques",
      "concrete examples",
      "general question"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}