{
  "id": "math/0403127",
  "version": "v2",
  "published": "2004-03-08T10:15:12.000Z",
  "updated": "2005-04-01T07:33:24.000Z",
  "title": "Expanders, rank and graphs of groups",
  "authors": [
    "Marc Lackenby"
  ],
  "comment": "13 pages; to appear in Israel J. Math",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "Let G be a finitely presented group, and let {G_i} be a collection of finite index normal subgroups that is closed under intersections. Then, we prove that at least one of the following must hold: 1. G_i is an amalgamated free product or HNN extension, for infinitely many i; 2. the Cayley graphs of G/G_i (with respect to a fixed finite set of generators for G) form an expanding family; 3. inf_i (d(G_i)-1)/[G:G_i] = 0, where d(G_i) is the rank of G_i. The proof involves an analysis of the geometry and topology of finite Cayley graphs. Several applications of this result are given.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-04-01T07:33:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20E06",
      "20F05",
      "05C25"
    ],
    "keywords": [
      "finite index normal subgroups",
      "finite cayley graphs",
      "hnn extension",
      "fixed finite set",
      "amalgamated free product"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......3127L"
    }
  }
}