{
  "id": "1209.6532",
  "version": "v1",
  "published": "2012-09-28T14:23:57.000Z",
  "updated": "2012-09-28T14:23:57.000Z",
  "title": "On knots and links in lens spaces",
  "authors": [
    "Alessia Cattabriga",
    "Enrico Manfredi",
    "Michele Mulazzani"
  ],
  "comment": "23 pages, 19 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "In this paper we study some aspects of knots and links in lens spaces. Namely, if we consider lens spaces as quotient of the unit ball $B^{3}$ with suitable identification of boundary points, then we can project the links on the equatorial disk of $B^{3}$, obtaining a regular diagram for them. In this contest, we obtain a complete finite set of Reidemeister type moves establishing equivalence, up to ambient isotopy, a Wirtinger type presentation for the fundamental group of the complement of the link and a diagrammatic method giving the first homology group. We also compute Alexander polynomial and twisted Alexander polynomials of this class of links, showing their correlation with Reidemeister torsion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-09-28T14:23:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27",
      "57M05"
    ],
    "keywords": [
      "lens spaces",
      "alexander polynomial",
      "reidemeister type moves establishing equivalence",
      "complete finite set",
      "wirtinger type presentation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.6532C"
    }
  }
}