{
  "id": "1101.1843",
  "version": "v5",
  "published": "2011-01-10T15:17:26.000Z",
  "updated": "2018-10-08T15:42:21.000Z",
  "title": "Asymptotic dimension and the disk graph I",
  "authors": [
    "Ursula Hamenstaedt"
  ],
  "comment": "17 pages, 1 figure",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "For a 3-manifold M and a subsurface $X$ of the boundary of M with empty or incompressible boundary we use surgery to identify a graph whose vertices are disks with boundary in X and which is quasi-isometrically embedded in the curve graph of X.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2014-02-22T22:00:27.000Z",
      "title": "Geometry of graphs of discs in a handlebody: Surgery and intersection",
      "abstract": "For a handlebody H of genus g>1 we use surgery to identify a graph whose vertices are discs and which is quasi-isometrically embedded in the curve graph of the boundary surface.",
      "comment": "25 pages, 2 figures. Paper split into three parts. This is now the first part",
      "journal": null,
      "doi": null
    },
    {
      "version": "v5",
      "updated": "2018-10-08T15:42:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M99",
      "20E36"
    ],
    "keywords": [
      "handlebody",
      "intersection",
      "curve graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1101.1843H"
    }
  }
}