{
  "id": "math/9808064",
  "version": "v3",
  "published": "1998-08-14T21:19:47.000Z",
  "updated": "1999-06-20T00:00:00.000Z",
  "title": "R-covered foliations of hyperbolic 3-manifolds",
  "authors": [
    "Danny Calegari"
  ],
  "comment": "17 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol3/paper6.abs.html",
  "journal": "Geom. Topol. 3 (1999), 137-153",
  "categories": [
    "math.GT"
  ],
  "abstract": "We produce examples of taut foliations of hyperbolic 3-manifolds which are R-covered but not uniform --- ie the leaf space of the universal cover is R, but pairs of leaves are not contained in bounded neighborhoods of each other. This answers in the negative a conjecture of Thurston `Three-manifolds, foliations and circles I' (math.GT/9712268). We further show that these foliations can be chosen to be C^0 close to foliations by closed surfaces. Our construction underscores the importance of the existence of transverse regulating vector fields and cone fields for R-covered foliations. Finally, we discuss the effect of perturbing arbitrary R-covered foliations.",
  "revisions": [
    {
      "version": "v3",
      "updated": "1999-06-20T00:00:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50",
      "57R30",
      "53C12"
    ],
    "keywords": [
      "hyperbolic",
      "transverse regulating vector fields",
      "produce examples",
      "cone fields",
      "taut foliations"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}