{
  "id": "1107.0672",
  "version": "v3",
  "published": "2011-07-04T16:14:04.000Z",
  "updated": "2011-09-12T20:34:56.000Z",
  "title": "Centralizers in R. Thompson's group V_n",
  "authors": [
    "Collin Bleak",
    "Hannah Bowman",
    "Alison Gordon",
    "Garrett Graham",
    "Jacob Hughes",
    "Francesco Matucci",
    "Jenya Sapir"
  ],
  "comment": "32 pages, 18 figures. Added a reference in the introduction",
  "categories": [
    "math.GR",
    "math.DS"
  ],
  "abstract": "Let n be bigger than 1 and let A be an element in the Higman-Thompson group V_n. We study the structure of the centralizer of a in V_n through a careful analysis of the action of the group generated by A on the Cantor set C. We make use of revealing tree pairs as developed by Brin and Salazar from which we derive discrete train tracks to assist us in our analysis. A consequence of our structure theorem is that centralizers are finitely generated. Along the way we give a short argument using revealing tree pairs which shows that cyclic groups are undistorted in V_n.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-09-12T20:34:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20E07",
      "37C85"
    ],
    "keywords": [
      "thompsons group",
      "centralizer",
      "revealing tree pairs",
      "derive discrete train tracks",
      "short argument"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.0672B"
    }
  }
}