{
  "id": "1708.00718",
  "version": "v1",
  "published": "2017-08-02T12:18:45.000Z",
  "updated": "2017-08-02T12:18:45.000Z",
  "title": "On a rigidity property of perturbations of circle bundles on 3-manifolds",
  "authors": [
    "Massimo Villarini"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We show that a smooth 1-parameter family of foliations by circles of a closed 3-manifold, deforming the foliation whose leaves are the fibers of a circle bundle, is trivial, i.e. all the foliations of the family arise from circle bundles isomorphic to the unperturbed one, if a continuity property of the Seifert leaves of the perturbation holds true. This rigidity property is true for any real analytic 1-parameter family of foliations by circles when the base space of the circle bundle defining the unperturbed foliation is not a torus. The dimensionality hypothesis is discussed in relation to an example by Thurston of a vector field on a closed 5-manifold whose orbits are closed, with unbounded lenght.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-02T12:18:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rigidity property",
      "circle bundles isomorphic",
      "perturbation holds true",
      "vector field",
      "continuity property"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}