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Geodesic laminations on compact surfaces and homeomorphisms of the Cantor set. (English) Zbl 1169.57303

Summary: In this paper we investigate a connection between minimal geodesic laminations on compact hyperbolic surfaces and homeomorphisms of the Cantor set. Let \(M\) be a compact hyperbolic surface. To each minimal lamination \({\mathcal L}\subset M\) having no closed leaves, and to each compact curve \(C\) transverse to \(\mathcal L\), we associate a group consisting of certain homeomorphisrns on the intersection \(C\cap{\mathcal L}\). This group is used to study various topological aspects of the lamination including orientability and existence of transverse measures.

MSC:

57M50 General geometric structures on low-dimensional manifolds
37C85 Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\)
57N05 Topology of the Euclidean \(2\)-space, \(2\)-manifolds (MSC2010)
57R30 Foliations in differential topology; geometric theory
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References:

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