{
  "id": "math/9906182",
  "version": "v1",
  "published": "1999-06-27T03:42:16.000Z",
  "updated": "1999-06-27T03:42:16.000Z",
  "title": "Lower bounds on volumes of hyperbolic Haken 3-manifolds",
  "authors": [
    "Ian Agol"
  ],
  "comment": "20 pages, 15 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "In this paper, we find lower bounds for volumes of hyperbolic 3-manifolds with various topological conditions. Let V_3 = 1.01494 denote the volume of a regular ideal simplex in hyperbolic 3-space. As a special case of the main theorem, if a hyperbolic manifold M contains an acylindrical surface S, then Vol(M)>= -2 V_3 chi(S). We also show that if beta_1(M)>= 2, then Vol(M)>= 4/5 V_3.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-06-27T03:42:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50"
    ],
    "keywords": [
      "lower bounds",
      "hyperbolic haken",
      "regular ideal simplex",
      "hyperbolic manifold",
      "special case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......6182A"
    }
  }
}