{
  "id": "math/0606381",
  "version": "v3",
  "published": "2006-06-15T22:08:15.000Z",
  "updated": "2008-10-23T09:16:16.000Z",
  "title": "A 1-parameter approach to links in a solid torus",
  "authors": [
    "T. Fiedler",
    "V. Kurlin"
  ],
  "comment": "38 pages, 14 figures, the applications on closed braids were moved to another paper `Recognising trace graphs of closed braids' (arXiv:0808.2713), more details were added on versal deformations of codimension 2 singularities",
  "categories": [
    "math.GT"
  ],
  "abstract": "To an oriented link in a solid torus we associate a trace graph in a thickened torus in such a way that links are isotopic if and only if their trace graphs can be related by moves of finitely many standard types. The key ingredient is a study of codimension~2 singularities of link diagrams. For closed braids with a fixed number of strands, trace graphs can be recognized up to equivalence excluding one type of moves in polynomial time with respect to the braid length.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-10-23T09:16:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R45",
      "57M25",
      "53A04"
    ],
    "keywords": [
      "solid torus",
      "trace graph",
      "standard types",
      "braid length",
      "link diagrams"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......6381F"
    }
  }
}