{
  "id": "1910.13839",
  "version": "v1",
  "published": "2019-10-30T13:24:09.000Z",
  "updated": "2019-10-30T13:24:09.000Z",
  "title": "Every noncompact surface is a leaf of a minimal foliation",
  "authors": [
    "Paulo Gusmão",
    "Carlos Meniño Cotón"
  ],
  "comment": "41 pages, 8 figures",
  "categories": [
    "math.GT",
    "math.DS"
  ],
  "abstract": "We show that any noncompact oriented surface is homeomorphic to the leaf of a minimal foliation of a closed $3$-manifold. Some of these foliations are suspensions of continuous minimal actions of surface groups. Moreover, the above result is also true for any prescription of a countable family of topologies of open surfaces: they can coexist in the same minimal foliation. All the given examples are hyperbolic foliations, meaning that they admit a leafwise Riemannian metric of constant negative curvature. Many oriented Seifert manifolds with a fibered incompressible torus, trivial euler class and whose associated orbifold is hyperbolic admit minimal foliations as above. The given examples are not transversely $C^2$-smoothable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-30T13:24:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R30",
      "37C85"
    ],
    "keywords": [
      "noncompact surface",
      "hyperbolic admit minimal foliations",
      "trivial euler class",
      "leafwise riemannian metric",
      "surface groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}