{
  "id": "1510.06292",
  "version": "v1",
  "published": "2015-10-21T15:13:01.000Z",
  "updated": "2015-10-21T15:13:01.000Z",
  "title": "Norms on the cohomology of hyperbolic 3-manifolds",
  "authors": [
    "Jeffrey F. Brock",
    "Nathan M. Dunfield"
  ],
  "comment": "26 pages, 2 figures",
  "categories": [
    "math.GT",
    "math.DG",
    "math.NT"
  ],
  "abstract": "We study the relationship between two norms on the first cohomology of a hyperbolic 3-manifold: the purely topological Thurston norm and the more geometric harmonic norm. Refining recent results of Bergeron, \\c{S}eng\\\"un, and Venkatesh, we show that these norms are roughly proportional with explicit constants depending only on the volume and injectivity radius of the hyperbolic 3-manifold itself. Moreover, we give families of examples showing that some (but not all) qualitative aspects of our estimates are sharp. Finally, we exhibit closed hyperbolic 3-manifolds where the Thurston norm grows exponentially in terms of the volume and yet there is a uniform lower bound on the injectivity radius.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-21T15:13:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50",
      "30F40"
    ],
    "keywords": [
      "hyperbolic",
      "injectivity radius",
      "geometric harmonic norm",
      "thurston norm grows",
      "uniform lower bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151006292B"
    }
  }
}