{
  "id": "math/0703708",
  "version": "v1",
  "published": "2007-03-23T19:00:16.000Z",
  "updated": "2007-03-23T19:00:16.000Z",
  "title": "Finite covers of the infinite cyclic cover of a knot",
  "authors": [
    "J. O. Button"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "We show that the commutator subgroup G' of a classical knot group G need not have subgroups of every finite index, but it will if G' has a surjective homomorphism to the integers and we give an exact criterion for that to happen. We also give an example of a smoothly knotted n-sphere in the (n+2)-sphere for all n at least 2 whose infinite cyclic cover is not simply connected but has no proper finite covers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-03-23T19:00:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57Q45"
    ],
    "keywords": [
      "infinite cyclic cover",
      "proper finite covers",
      "commutator subgroup",
      "finite index",
      "classical knot group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......3708B"
    }
  }
}