{
  "id": "math/0404525",
  "version": "v1",
  "published": "2004-04-29T10:14:45.000Z",
  "updated": "2004-04-29T10:14:45.000Z",
  "title": "Hyperbolic dimension of metric spaces",
  "authors": [
    "S. Buyalo",
    "V. Schroeder"
  ],
  "comment": "18 pages",
  "journal": "St. Petersburg Math. J. 19 (2008), no. 1, 67--76.",
  "categories": [
    "math.GT",
    "math.MG"
  ],
  "abstract": "We introduce a new quasi-isometry invariant of metric spaces called the hyperbolic dimension, hypdim, which is a version of the Gromov's asymptotic dimension, asdim. The hyperbolic dimension is at most the asymptotic dimension, however, unlike the asymptotic dimension, the hyperbolic dimension of any Euclidean space R^n is zero (while asdim R^n=n.) This invariant possesses usual properties of dimension like monotonicity and product theorems. Our main result says that the hyperbolic dimension of any Gromov hyperbolic space X (with mild restrictions) is at least the topological dimension of the boundary at infinity plus 1. As an application we obtain that there is no quasi-isometric embedding of the real hyperbolic space H^n into the (n-1)-fold metric product of metric trees stabilized by any Euclidean factor.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-04-29T10:14:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54C25",
      "54E40",
      "51M10",
      "51Fxx"
    ],
    "keywords": [
      "hyperbolic dimension",
      "metric spaces",
      "invariant possesses usual properties",
      "main result says",
      "gromovs asymptotic dimension"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......4525B"
    }
  }
}