{
  "id": "1310.0936",
  "version": "v4",
  "published": "2013-10-03T10:20:56.000Z",
  "updated": "2015-05-23T13:01:28.000Z",
  "title": "Double Centralizers of Parabolic Subgroups of Braid Groups",
  "authors": [
    "David Garber",
    "Arkadius Kalka",
    "Eran Liberman",
    "Mina Teicher"
  ],
  "comment": "19 pages, 7 figures. We generalized the result to all parabolic subgroups. We also changed the title",
  "categories": [
    "math.GR",
    "math.AT"
  ],
  "abstract": "We characterize the double centralizer of all parabolic subgroups of the braid groups. We apply this result to provide a new and potentially more efficient solution to the subgroup conjugacy problem for parabolic subgroups. In the course of the proof we also characterize the centralizer for all parabolic subgroups which seems to have been done so far only for parabolic subgroups with connected associated Coxeter graph.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-03-25T14:41:06.000Z",
      "title": "Centralizers of Centralizers of Parabolic Subgroups of Braid Groups",
      "abstract": "We characterize the centralizer of the centralizer of all parabolic subgroups of the braid group having connected associated Coxeter graphs. We apply this result to provide a new and potentially more efficient solution to the subgroup conjugacy problem for these parabolic subgroups.",
      "comment": "13 pages. We made some minor changes and added figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2015-05-23T13:01:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F36"
    ],
    "keywords": [
      "parabolic subgroups",
      "centralizer",
      "braid group",
      "subgroup conjugacy problem",
      "connected associated coxeter graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.0936G"
    }
  }
}