{
  "id": "2101.10316",
  "version": "v1",
  "published": "2021-01-25T18:55:45.000Z",
  "updated": "2021-01-25T18:55:45.000Z",
  "title": "Conjugator length in Thompson's groups",
  "authors": [
    "James Belk",
    "Francesco Matucci"
  ],
  "comment": "13 pages, 8 figures",
  "categories": [
    "math.GR"
  ],
  "abstract": "We prove Thompson's group $F$ has quadratic conjugator length function. That is, for any two conjugate elements of $F$ of length $n$ or less, there exists an element of $F$ of length $O(n^2)$ that conjugates one to the other. Moreover, there exist conjugate pairs of elements of $F$ of length at most $n$ such that the shortest conjugator between them has length $\\Omega(n^2)$. This latter statement holds for $T$ and $V$ as well.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-25T18:55:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F10",
      "20F65",
      "20E45"
    ],
    "keywords": [
      "thompsons group",
      "quadratic conjugator length function",
      "shortest conjugator",
      "statement holds",
      "conjugate elements"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}