{
  "id": "1609.05154",
  "version": "v1",
  "published": "2016-09-16T17:49:32.000Z",
  "updated": "2016-09-16T17:49:32.000Z",
  "title": "Relatively hyperbolic groups with fixed peripherals",
  "authors": [
    "Matthew Cordes",
    "David Hume"
  ],
  "comment": "20 pages, 2 figures",
  "categories": [
    "math.GR",
    "math.GT",
    "math.MG"
  ],
  "abstract": "We build quasi--isometry invariants of relatively hyperbolic groups which detect the hyperbolic parts of the group; these are variations of the stable dimension constructions previously introduced by the authors. We prove that, given any finite collection of finitely generated groups $\\mathcal{H}$ each of which either has finite stable dimension or is non-relatively hyperbolic, there exist infinitely many quasi--isometry types of one--ended groups which are hyperbolic relative to $\\mathcal{H}$. The groups are constructed using small cancellation theory over free products.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-16T17:49:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20F67"
    ],
    "keywords": [
      "relatively hyperbolic groups",
      "fixed peripherals",
      "build quasi-isometry invariants",
      "small cancellation theory",
      "free products"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}