{
  "id": "math/9907058",
  "version": "v1",
  "published": "1999-07-09T17:41:11.000Z",
  "updated": "1999-07-09T17:41:11.000Z",
  "title": "Injectivity Radius Bounds in Hyperbolic Convex Cores I",
  "authors": [
    "Carol E. Fan"
  ],
  "comment": "23 pages, 1 figure",
  "categories": [
    "math.GT",
    "math.GN"
  ],
  "abstract": "A version of a conjecture of McMullen is as follows: Given a hyperbolizable 3-manifold M with incompressible boundary, there exists a uniform constant K such that if N is a hyperbolic 3-manifold homeomorphic to the interior of M, then the injectivity radius based at points in the convex core of N is bounded above by K. This conjecture suggests that convex cores are uniformly congested. In previous work, the author has proven the conjecture for $I$-bundles over a closed surface, taking into account the possibility of cusps. In this paper, we establish the conjecture in the case that M is a book of I-bundles or an acylindrical, hyperbolizable 3-manifold. In particular, we show that if M is a book of I-bundles, then the bound on injectivity radius depends on the number of generators in the fundamental group of M.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-07-09T17:41:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50",
      "30F40",
      "57N10"
    ],
    "keywords": [
      "hyperbolic convex cores",
      "injectivity radius bounds",
      "conjecture",
      "injectivity radius depends",
      "fundamental group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......7058F"
    }
  }
}