{
  "id": "0706.2740",
  "version": "v2",
  "published": "2007-06-19T09:03:32.000Z",
  "updated": "2010-01-09T15:45:49.000Z",
  "title": "Mapping Class Groups and Interpolating Complexes: Rank",
  "authors": [
    "Mahan Mj"
  ],
  "comment": "v2 Final version incorporating refree comments 16pgs no figs",
  "journal": "J. Ramanujan Math. Soc. 24, No.4 (2009) 341-357",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "A family of interpolating graphs $\\calC (S, \\xi)$ of complexity $\\xi$ is constructed for a surface $S$ and $-2 \\leq \\xi \\leq \\xi (S)$. For $\\xi = -2, -1, \\xi (S) -1$ these specialise to graphs quasi-isometric to the marking graph, the pants graph and the curve graph respectively. We generalise Theorems of Brock-Farb and Behrstock-Minsky to show that the rank of $\\calC (S, \\xi)$ is $r_\\xi$, the largest number of disjoint copies of subsurfaces of complexity greater than $\\xi $ that may be embedded in $S$. The interpolating graphs $\\calC (S, \\xi)$ interpolate between the pants graph and the curve graph.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-01-09T15:45:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F67",
      "22E40"
    ],
    "keywords": [
      "mapping class groups",
      "interpolating complexes",
      "pants graph",
      "interpolating graphs",
      "disjoint copies"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0706.2740M"
    }
  }
}