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Cantor Laminations and Exceptional Minimal Sets in Codimension One Foliations

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Geometry and its Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 72))

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Abstract

In this paper we deal with two types of questions concerning the structure of foliations (or laminations) on compact spaces:

  1. 1.

    Describe generic properties of foliations and laminations and refine the known ones,

  2. 2.

    Discuss the embeddability of n-dimensional minimal Cantor laminations as minimal sets in codimension one foliations on compact (n + 1)-manifolds or as closed sets in \({\mathbb{R}}^{n+1}\) (or any simply connected (n + 1)-manifold).

The two questions are related by the fact that exceptional minimal sets in codimension one present stronger generic constraints.

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Author information

Authors and Affiliations

  1. Institut C. Jordan UMR CNRS 5208, Université C. Bernard bât 101, 43 Boulevard du 11 novembre 1918, 69622, Villeurbanne Cedex, France

    Gilbert Hector

Authors
  1. Gilbert Hector
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Correspondence to Gilbert Hector .

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Editors and Affiliations

  1. Department of Mathematics, University of Haifa, Haifa, Israel

    Vladimir Rovenski

  2. Faculty of Mathematics, University of Łód´z', Łód´z', Poland

    Paweł Walczak

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Hector, G. (2014). Cantor Laminations and Exceptional Minimal Sets in Codimension One Foliations. In: Rovenski, V., Walczak, P. (eds) Geometry and its Applications. Springer Proceedings in Mathematics & Statistics, vol 72. Springer, Cham. https://doi.org/10.1007/978-3-319-04675-4_3

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