{
  "id": "1510.07156",
  "version": "v1",
  "published": "2015-10-24T15:51:21.000Z",
  "updated": "2015-10-24T15:51:21.000Z",
  "title": "Existence and non-existence of bounded packing in CAT(0) spaces and Gromov hyperbolic spaces",
  "authors": [
    "Pranab Sardar"
  ],
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "The main result of this paper is that given a group $G$ acting geometrically by isometries on a CAT(0) space $X$ and a cyclic subgroup $H$ of $G$ generated by a rank-1 isometry of $X$, $H$ has bounded packing in $G$. We give two proofs of this result. The first one is by a characterization of rank-$1$ isometries by Hamenstadt. The second proof follows directly from some results of Dahmani-Guirardel-Osin and Sisto. Then using Mihailova's construction, we show the existence of a finitely generated subgroup of the direct product of two free groups $\\mathbb F_2\\times \\mathbb F_2$ without the bounded packing property answering a question of Hruska-Wise. We also prove the existence of finitely presented subgroups of CAT(0) groups without bounded packing using Wise's {\\em modified Rip's construction} and the {\\bf 1-2-3} theorem of Baumslag, Bridson, Miller and Short.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-24T15:51:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gromov hyperbolic spaces",
      "bounded packing",
      "non-existence",
      "cyclic subgroup",
      "main result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151007156S"
    }
  }
}