{
  "id": "1501.07001",
  "version": "v1",
  "published": "2015-01-28T06:32:54.000Z",
  "updated": "2015-01-28T06:32:54.000Z",
  "title": "Quantifying separability in virtually special groups",
  "authors": [
    "Mark F. Hagen",
    "Priyam Patel"
  ],
  "comment": "12 pages, 5 figures",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "We give a new, effective proof of the separability of cubically convex-cocompact subgroups of special groups. As a consequence, we show that if $G$ is a virtually compact special hyperbolic group, and $Q\\leq G$ is a $K$-quasiconvex subgroup, then any $g\\in G-Q$ of word-length at most $n$ is separated from $Q$ by a subgroup whose index is polynomial in $n$ and exponential in $K$. This generalizes a result of Bou-Rabee and the authors on residual finiteness growth and a result of the second author on surface groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-28T06:32:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E26",
      "20F36"
    ],
    "keywords": [
      "virtually special groups",
      "quantifying separability",
      "virtually compact special hyperbolic group",
      "residual finiteness growth",
      "second author"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150107001H"
    }
  }
}