{
  "id": "2004.01471",
  "version": "v1",
  "published": "2020-04-03T11:11:19.000Z",
  "updated": "2020-04-03T11:11:19.000Z",
  "title": "The computational complexity of determining knot genus in a fixed 3-manifold",
  "authors": [
    "Marc Lackenby",
    "Mehdi Yazdi"
  ],
  "comment": "38 pages, 6 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We show that the problem of determining the genus of a knot in a fixed compact, orientable three-dimensional manifold lies in NP. This answers a question asked by Agol, Hass, and Thurston in 2002. Previously, this was known for rational homology three-spheres, by the work of the first author.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-03T11:11:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57N10",
      "57M27",
      "68Q15",
      "68Q17",
      "57M25"
    ],
    "keywords": [
      "determining knot genus",
      "computational complexity",
      "rational homology three-spheres",
      "orientable three-dimensional manifold lies",
      "first author"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}