{
  "id": "math/0111209",
  "version": "v3",
  "published": "2001-11-19T18:11:43.000Z",
  "updated": "2002-04-11T13:16:46.000Z",
  "title": "Linking numbers of measured foliations",
  "authors": [
    "D. Kotschick",
    "T. Vogel"
  ],
  "comment": "minor corrections, to appear in Ergodic Theory and Dynamical Systems",
  "journal": "Ergodic Theory Dynam. Systems 23 (2003), 541--558.",
  "doi": "10.1017/S0143385702001219",
  "categories": [
    "math.GT",
    "math.DS"
  ],
  "abstract": "We generalise the average asymptotic linking number of a pair of divergence-free vector fields on homology three-spheres by considering the linking of a divergence-free vector field on a manifold of arbitrary dimension with a codimension two foliation endowed with an invariant transverse measure. We prove that the average asymptotic linking number is given by an integral of Hopf type. Considering appropriate vector fields and measured foliations, we obtain an ergodic interpretation of the Godbillon-Vey invariant of a family of codimension one foliations discussed in math.GT/0111137.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2002-04-11T13:16:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R30",
      "37C10",
      "37C40",
      "37C85"
    ],
    "keywords": [
      "measured foliations",
      "average asymptotic linking number",
      "divergence-free vector field",
      "invariant transverse measure",
      "considering appropriate vector fields"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math.....11209K"
    }
  }
}