{
  "id": "2103.01325",
  "version": "v1",
  "published": "2021-03-01T21:47:23.000Z",
  "updated": "2021-03-01T21:47:23.000Z",
  "title": "Reeb flows transverse to foliations",
  "authors": [
    "Jonathan Zung"
  ],
  "comment": "24 pages, 3 figures",
  "categories": [
    "math.GT",
    "math.SG"
  ],
  "abstract": "Let $\\mathcal F$ be a co-oriented $C^2$ foliation on a closed, oriented 3-manifold. We show that $T\\mathcal F$ can be perturbed to a contact structure with Reeb flow transverse to $\\mathcal F$ if and only if $\\mathcal F$ does not support an invariant transverse measure. The resulting Reeb flow has no contractible orbits. This answers a question of Colin and Honda. The main technical tool in our proof is leafwise Brownian motion which we use to construct good transverse measures for $\\mathcal F$; this gives a new perspective on the Eliashberg--Thurston theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-01T21:47:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R30",
      "57K33"
    ],
    "keywords": [
      "reeb flows transverse",
      "reeb flow transverse",
      "invariant transverse measure",
      "eliashberg-thurston theorem",
      "resulting reeb flow"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}