{
  "id": "1608.07258",
  "version": "v1",
  "published": "2016-08-25T19:19:49.000Z",
  "updated": "2016-08-25T19:19:49.000Z",
  "title": "Centralizers in the Group of Interval Exchange Transformations",
  "authors": [
    "Daniel Bernazzani"
  ],
  "comment": "12 pages",
  "categories": [
    "math.DS",
    "math.GR"
  ],
  "abstract": "Let $T$ be an $m$-interval exchange transformation. By the rank of $T$ we mean the dimension of the $\\mathbb{Q}$-vector space spanned by the lengths of the exchanged subintervals. We prove that if $T$ satisfies Keane's infinite distinct orbit condition and $\\text{rank}(T)>1+\\lfloor m/2 \\rfloor$ then the only interval exchange transformations which commute with $T$ are its powers. The main step in our proof is to show that the centralizer of $T$ is torsion-free under the above hypotheses.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-25T19:19:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "interval exchange transformation",
      "satisfies keanes infinite distinct orbit",
      "centralizer",
      "keanes infinite distinct orbit condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}