{
  "id": "1602.04863",
  "version": "v1",
  "published": "2016-02-15T23:14:47.000Z",
  "updated": "2016-02-15T23:14:47.000Z",
  "title": "Dismantlable classifying space for the family of parabolic subgroups of a relatively hyperbolic group",
  "authors": [
    "Eduardo Martinez-Pedroza",
    "Piotr Przytycki"
  ],
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "Let $G$ be a group hyperbolic relative to a finite collection of subgroups $\\mathcal P$. Let $\\mathcal F$ be the family of subgroups consisting of all the conjugates of subgroups in $\\mathcal P$, all their subgroups, and all finite subgroups. Then there is a cocompact model for $E_{\\mathcal F} G$. This result was known in the torsion-free case. In the presence of torsion, a new approach was necessary. Our method is to exploit the notion of dismantlability. A number of sample applications are discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-15T23:14:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F67",
      "57M07",
      "55R35",
      "57S30"
    ],
    "keywords": [
      "relatively hyperbolic group",
      "dismantlable classifying space",
      "parabolic subgroups",
      "group hyperbolic",
      "finite collection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160204863M"
    }
  }
}