Every noncompact surface is a leaf of a minimal foliation
Paulo Gusmão
Universidade Federal Fluminense, Niterói, BrazilCarlos Meniño Cotón
Universidade de Vigo, Vigo, Spain; CITMAGA (Centro de Investigación y Tecnología Matemática de Galicia), Santiago de Compostela, Spain
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Abstract
We show that any noncompact oriented surface is homeomorphic to the leaf of a minimal foliation of a closed -manifold. These foliations are (or are covered by) suspensions of continuous minimal actions of surface groups on the circle. Moreover, the above result is also true for any prescription of a countable family of topologies of noncompact 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 and whose associated orbifold is hyperbolic admit minimal foliations as above. The given examples are not transversely -smoothable.
Cite this article
Paulo Gusmão, Carlos Meniño Cotón, Every noncompact surface is a leaf of a minimal foliation. Rev. Mat. Iberoam. 40 (2024), no. 4, pp. 1207–1248
DOI 10.4171/RMI/1486