{
  "id": "1709.09024",
  "version": "v1",
  "published": "2017-09-23T07:31:32.000Z",
  "updated": "2017-09-23T07:31:32.000Z",
  "title": "Limits of conjugacy classes under iterates of Hyperbolic elements of $\\mathsf{Out(\\mathbb{F})}$",
  "authors": [
    "Pritam Ghosh"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1306.6049",
  "categories": [
    "math.GR"
  ],
  "abstract": "For a free group $\\mathbb{F}$ of finite rank such that $\\text{rank}(\\mathbb{F})\\geq 3$, we prove that the set of weak limits of a conjugacy class in $\\mathbb{F}$ under iterates of some hyperbolic $\\phi\\in\\mathsf{Out(\\mathbb{F})}$ is equal to the collection of generic leaves and singular lines of $\\phi$. As an application we describe the ending lamination set for a hyperbolic extension of $\\mathbb{F}$ by a hyperbolic subgroup of $\\mathsf{Out(\\mathbb{F})}$ in a new way and use it to prove results about Cannon-Thurston maps for such extensions. We also use it to derive conditions for quasiconvexity of finitely generated, infinite index subgroups of $\\mathbb{F}$ in the extension group. These results generalize similar results obtained by Mahan Mj, Kapovich-Lustig and use different techniques.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-23T07:31:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65"
    ],
    "keywords": [
      "conjugacy class",
      "hyperbolic elements",
      "results generalize similar results",
      "infinite index subgroups",
      "lamination set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}