{
  "id": "math/0512356",
  "version": "v2",
  "published": "2005-12-15T10:35:39.000Z",
  "updated": "2007-03-29T09:33:44.000Z",
  "title": "Adding high powered relations to large groups",
  "authors": [
    "Marc Lackenby"
  ],
  "comment": "15 pages, 7 figures; v2: minor corrections and improved exposition; to appear in Mathematical Research Letters",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "A group is known as `large' if some finite index subgroup admits a surjective homomorphism onto a non-abelian free group. The main theorem of the paper is as follows. Let G be a finitely generated, large group and let g_1,...,g_r be a collection of elements of G. Then G/<<g_1^n,...,g_r^n>> is also large, for infinitely many integers n. Furthermore, when G is free, this holds for all but finitely many n. These results have the following application to Dehn surgery. Let M be a compact orientable 3-manifold with boundary a torus. Suppose that the 3-manifold obtained by Dehn filling some slope on the boundary has large fundamental group. Then this is true for infinitely many filling slopes.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-03-29T09:33:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "57M07",
      "57N10"
    ],
    "keywords": [
      "adding high powered relations",
      "large group",
      "finite index subgroup admits",
      "large fundamental group",
      "non-abelian free group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....12356L"
    }
  }
}