{
  "id": "math/0609616",
  "version": "v2",
  "published": "2006-09-21T16:30:21.000Z",
  "updated": "2007-02-22T23:10:18.000Z",
  "title": "Conjugacy in Garside Groups III: Periodic braids",
  "authors": [
    "Joan S. Birman",
    "Volker Gebhardt",
    "Juan Gonzalez-Meneses"
  ],
  "comment": "33 pages, 13 figures. Classical references implying Corollaries 12 and 15 have been added. To appear in Journal of Algebra",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "An element in Artin's braid group B_n is said to be periodic if some power of it lies in the center of B_n. In this paper we prove that all previously known algorithms for solving the conjugacy search problem in B_n are exponential in the braid index n for the special case of periodic braids. We overcome this difficulty by putting to work several known isomorphisms between Garside structures in the braid group B_n and other Garside groups. This allows us to obtain a polynomial solution to the original problem in the spirit of the previously known algorithms. This paper is the third in a series of papers by the same authors about the conjugacy problem in Garside groups. They have a unified goal: the development of a polynomial algorithm for the conjugacy decision and search problems in B_n, which generalizes to other Garside groups whenever possible. It is our hope that the methods introduced here will allow the generalization of the results in this paper to all Artin-Tits groups of spherical type.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-02-22T23:10:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F36",
      "20F10"
    ],
    "keywords": [
      "garside groups",
      "periodic braids",
      "conjugacy search problem",
      "artins braid group",
      "artin-tits groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9616B"
    }
  }
}