{
  "id": "1207.3008",
  "version": "v2",
  "published": "2012-07-12T16:04:57.000Z",
  "updated": "2013-10-24T12:00:38.000Z",
  "title": "Embedding relatively hyperbolic groups in products of trees",
  "authors": [
    "John M. Mackay",
    "Alessandro Sisto"
  ],
  "comment": "v1: 18 pages; v2: 20 pages, minor changes",
  "journal": "Alg. Geom. Top., Volume 13 (2013) 2261-2282",
  "doi": "10.2140/agt.2013.13.2261",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "We show that a relatively hyperbolic group quasi-isometrically embeds in a product of finitely many trees if the peripheral subgroups do, and we provide an estimate on the minimal number of trees needed. Applying our result to the case of 3-manifolds, we show that fundamental groups of closed 3-manifolds have linearly controlled asymptotic dimension at most 8. To complement this result, we observe that fundamental groups of Haken 3-manifolds with non-empty boundary have asymptotic dimension 2.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-10-24T12:00:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20F69"
    ],
    "keywords": [
      "embedding relatively hyperbolic groups",
      "fundamental groups",
      "relatively hyperbolic group quasi-isometrically embeds",
      "peripheral subgroups",
      "non-empty boundary"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.3008M"
    }
  }
}