{
  "id": "1602.05884",
  "version": "v1",
  "published": "2016-02-18T17:36:24.000Z",
  "updated": "2016-02-18T17:36:24.000Z",
  "title": "An explicit relation between knot groups in lens spaces and those in $S^3$",
  "authors": [
    "Yuta Nozaki"
  ],
  "comment": "11 pages, no figure",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "We consider a cyclic covering map $(\\Sigma,K) \\to (\\Sigma',K')$ between pairs of a 3-manifold and a knot, and describe the fundamental group $\\pi_1(\\Sigma \\setminus K)$ in terms of $\\pi_1(\\Sigma' \\setminus K')$. As a consequence, we give an alternative proof for the fact that a certain knot in $S^3$ cannot be represented as the preimage of any knot in a lens space. In our proofs, the subgroup of a group $G$ generated by the commutators and the $p$th power of each element of $G$ plays a key role.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-18T17:36:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "lens space",
      "knot groups",
      "explicit relation",
      "cyclic covering map",
      "th power"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160205884N"
    }
  }
}