{
  "id": "0802.0033",
  "version": "v2",
  "published": "2008-01-31T23:25:01.000Z",
  "updated": "2008-08-20T16:43:57.000Z",
  "title": "Intersections and joins of free groups",
  "authors": [
    "Richard P. Kent IV"
  ],
  "comment": "18 pages, 4 figures. Referee's comments incorporated. To appear in Algebraic & Geometric Topology",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "Let H and K be subgroups of a free group of ranks h and k \\geq h. We prove the following strong form of Burns' inequality: rank(H \\cap K) - 1 \\leq 2(h-1)(k-1) - (h-1)(rank(H \\vee K) -1). A corollary of this, also obtained by L. Louder and D. B. McReynolds, has been used by M. Culler and P. Shalen to obtain information regarding the volumes of hyperbolic 3-manifolds. We also prove the following particular case of the Hanna Neumann Conjecture, which has also been obtained by Louder. If the join of H and K has rank at least (h + k + 1)/2, then the intersection of H and K has rank no more than (h-1)(k-1) + 1.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-08-20T16:43:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "free group",
      "intersection",
      "hanna neumann conjecture",
      "strong form",
      "mcreynolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0802.0033K"
    }
  }
}