On the homeomorphisms of the space of geodesic laminations on a hyperbolic surface

Charalampos Charitos (1) , Ioannis Papadoperakis (1) , Athanase Papadopoulos (2)

1 Laboratory of Mathematics
2 IRMA - Institut de Recherche Mathématique Avancée

We prove that for any orientable connected surface of finite type which is not a a sphere with at most four punctures or a torus with at most two punctures, any homeomorphism of the space of geodesic laminations of this surface, equipped with the Thurston topology, is induced by a homeomorphism of the surface.

Mots clés: Geodesic lamination; mapping class group; hyperbolic surface; Hausdorff topology; Thurston topology

Domaines: Topologie géométrique [math.GT]

Charalampos Charitos, Ioannis Papadoperakis, Athanase Papadopoulos. On the homeomorphisms of the space of geodesic laminations on a hyperbolic surface. Proceedings of the American Mathematical Society, 2014, 142, p. 2179-2191. ⟨10.1090/S0002-9939-2014-11934-4⟩. ⟨hal-00649664v3⟩