{
  "id": "math/0205138",
  "version": "v3",
  "published": "2002-05-13T21:43:23.000Z",
  "updated": "2004-04-06T10:49:19.000Z",
  "title": "(1,1)-knots via the mapping class group of the twice punctured torus",
  "authors": [
    "Alessia Cattabriga",
    "Michele Mulazzani"
  ],
  "comment": "18 pages, 10 figures. New version with minor changes. Accepted for publication in Advances in Geometry",
  "categories": [
    "math.GT"
  ],
  "abstract": "We develop an algebraic representation for (1,1)-knots using the mapping class group of the twice punctured torus MCG(T,2). We prove that every (1,1)-knot in a lens space L(p,q) can be represented by the composition of an element of a certain rank two free subgroup of MCG(T,2) with a standard element only depending on the ambient space. As a notable examples, we obtain a representation of this type for all torus knots and for all two-bridge knots. Moreover, we give explicit cyclic presentations for the fundamental groups of the cyclic branched coverings of torus knots of type (k,ck+2).",
  "revisions": [
    {
      "version": "v3",
      "updated": "2004-04-06T10:49:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M05",
      "20F38"
    ],
    "keywords": [
      "mapping class group",
      "torus knots",
      "twice punctured torus mcg",
      "explicit cyclic presentations",
      "algebraic representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......5138C"
    }
  }
}