{
  "id": "1404.5919",
  "version": "v3",
  "published": "2014-04-20T14:28:49.000Z",
  "updated": "2015-10-16T23:53:20.000Z",
  "title": "Approximating $C^{1,0}$-foliations",
  "authors": [
    "William H. Kazez",
    "Rachel Roberts"
  ],
  "comment": "52 pages, 5 figures. Final version with updated references, corrections and terminology",
  "categories": [
    "math.GT"
  ],
  "abstract": "We extend the Eliashberg-Thurston theorem on approximations of taut oriented $C^2$-foliations of 3-manifolds by both positive and negative contact structures to a large class of taut oriented $C^{1,0}$-foliations, where by $C^{1,0}$ foliation, we mean a foliation with continuous tangent plane field. These $C^{1,0}$-foliations can therefore be approximated by weakly symplectically fillable, universally tight, contact structures. This allows applications of $C^2$-foliation theory to contact topology and Floer theory to be generalized and extended to constructions of $C^{1,0}$-foliations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-31T14:24:48.000Z",
      "title": "Approximating $C^0$-foliations",
      "abstract": "We extend the Eliashberg-Thurston theorem on approximations of taut oriented $C^2$-foliations of 3-manifolds by both positive and negative contact structures to a large class of taut oriented $C^0$-foliations. These $C^0$-foliations can therefore be approximated by weakly symplectically fillable, and hence universally tight, contact structures. This allows applications of $C^2$-foliation theory to contact topology and Floer theory to be generalized and extended to constructions of $C^0$-foliations.",
      "comment": "50 pages, 5 figures. several improvements suggested by the referee have been made",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-10-16T23:53:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50",
      "53D10"
    ],
    "keywords": [
      "negative contact structures",
      "approximating",
      "eliashberg-thurston theorem",
      "large class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 52,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.5919K"
    }
  }
}