{
  "id": "math/0405502",
  "version": "v1",
  "published": "2004-05-26T16:14:06.000Z",
  "updated": "2004-05-26T16:14:06.000Z",
  "title": "Knot theory in handlebodies",
  "authors": [
    "Reinhard Haering-Oldenburg",
    "Sofia Lambropoulou"
  ],
  "comment": "23 pages, 23 figures, LaTex file",
  "journal": "J. Knot Theory and Ramifications, Vol. 11, No. 6, pp. 921--943 (2002)",
  "categories": [
    "math.GT",
    "math.AT"
  ],
  "abstract": "We consider oriented knots and links in a handlebody of genus $g$ through appropriate braid representatives in $S^3$, which are elements of the braid groups $B_{g,n}$. We prove a geometric version of the Markov theorem for braid equivalence in the handlebody, which is based on the $L$-moves. Using this we then prove two algebraic versions of the Markov theorem. The first one uses the $L$-moves. The second one uses the Markov moves and conjugation in the groups $B_{g,n}$. We show that not all conjugations correspond to isotopies.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-05-26T16:14:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25"
    ],
    "keywords": [
      "knot theory",
      "handlebody",
      "markov theorem",
      "appropriate braid representatives",
      "conjugations correspond"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......5502H"
    }
  }
}