{
  "id": "1312.1256",
  "version": "v1",
  "published": "2013-12-04T17:40:44.000Z",
  "updated": "2013-12-04T17:40:44.000Z",
  "title": "Lift in the 3-sphere of knots and links in lens spaces",
  "authors": [
    "Enrico Manfredi"
  ],
  "comment": "29 pages, 14 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "An important geometric invariant of links in lens spaces is the lift in the 3-sphere of a link $L$ in $L(p,q)$, that is the counterimage $\\widetilde L$ of $L$ under the universal covering of $L(p,q)$. If lens spaces are defined as a lens with suitable boundary identifications, then a link in $L(p,q)$ can be represented by a disk diagram, that is to say, a regular projection of the link on a disk. Starting from a disk diagram of $L$, we obtain a diagram of the lift $\\widetilde L$ in the 3-sphere. With this construction we are able to find different knots and links in $L(p,q)$ having equivalent lifts, that is to say, we cannot distinguish different links in lens spaces only from their lift.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-04T17:40:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27",
      "57M10"
    ],
    "keywords": [
      "lens spaces",
      "disk diagram",
      "important geometric invariant",
      "equivalent lifts",
      "regular projection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.1256M"
    }
  }
}