{
  "id": "1212.6749",
  "version": "v3",
  "published": "2012-12-30T17:17:41.000Z",
  "updated": "2015-02-05T16:59:41.000Z",
  "title": "Bounding the gap between a free group (outer) automorphism and its inverse",
  "authors": [
    "Manuel Ladra",
    "Pedro V. Silva",
    "Enric Ventura"
  ],
  "comment": "24 pages; To appear in Collectanea Mathematica",
  "doi": "10.1007/s13348-015-0133-3",
  "categories": [
    "math.GR"
  ],
  "abstract": "For any finitely generated group $G$, two complexity functions $\\alpha_G$ and $\\beta_G$ are defined to measure the maximal possible gap between the norm of an automorphism (respectively outer automorphism) of $G$ and the norm of its inverse. Restricting attention to free groups $F_r$, the exact asymptotic behaviour of $\\alpha_2$ and $\\beta_2$ is computed. For rank $r\\geqslant 3$, polynomial lower bounds are provided for $\\alpha_r$ and $\\beta_r$, and the existence of a polynomial upper bound is proved for $\\beta_r$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-04-30T18:04:16.000Z",
      "comment": "24 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-02-05T16:59:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E05",
      "20E36",
      "20F65"
    ],
    "keywords": [
      "free group",
      "exact asymptotic behaviour",
      "polynomial lower bounds",
      "polynomial upper bound",
      "complexity functions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.6749L"
    }
  }
}