{
  "id": "math/0509216",
  "version": "v4",
  "published": "2005-09-09T15:06:09.000Z",
  "updated": "2007-01-26T18:53:39.000Z",
  "title": "The asymptotic dimension of a curve graph is finite",
  "authors": [
    "Gregory Bell",
    "Koji Fujiwara"
  ],
  "comment": "19 pages. Made some minor revisions. The section on mapping class groups has been rewritten; in particular we compute the asdim of Mod(S) where S has genus at most 2. The last section on open questions has been modified to reflect recent developments. References have been updated",
  "doi": "10.1112/jlms/jdm090",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "We find an upper bound for the asymptotic dimension of a hyperbolic metric space with a set of geodesics satisfying a certain boundedness condition studied by Bowditch. The primary example is a collection of tight geodesics on the curve graph of a compact orientable surface. We use this to conclude that a curve graph has finite asymptotic dimension. It follows then that a curve graph has property $A_1$. We also compute the asymptotic dimension of mapping class groups of orientable surfaces with genus $\\le 2$.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2007-01-26T18:53:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M99",
      "20F69"
    ],
    "keywords": [
      "curve graph",
      "hyperbolic metric space",
      "finite asymptotic dimension",
      "upper bound",
      "primary example"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......9216B"
    }
  }
}