{
  "id": "1907.04430",
  "version": "v1",
  "published": "2019-07-09T21:56:17.000Z",
  "updated": "2019-07-09T21:56:17.000Z",
  "title": "A remark on thickness of free-by-cyclic groups",
  "authors": [
    "Mark Hagen"
  ],
  "comment": "9 pages, 0 figures. To appear in Illinois J. Math",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $F$ be a free group of positive, finite rank and let $\\Phi\\in Aut(F)$ be a polynomial-growth automorphism. Then $F\\rtimes_\\Phi\\mathbb Z$ is strongly thick of order $\\eta$, where $\\eta$ is the rate of polynomial growth of $\\phi$. This fact is implicit in work of Macura, but her work predates the notion of thickness. Therefore, in this note, we make the relationship between polynomial growth and thickness explicit. Our result combines with a result independently due to Dahmani-Li, Gautero-Lustig, and Ghosh to show that free-by-cyclic groups admit relatively hyperbolic structures with thick peripheral subgroups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-09T21:56:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "polynomial growth",
      "groups admit relatively hyperbolic structures",
      "free-by-cyclic groups admit relatively hyperbolic",
      "thick peripheral subgroups",
      "work predates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}