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A characterization of measured geodesic laminations of the pleating of hyperbolic manifolds, and their consequences. (Une caractérisation des laminations géodésiques mesurées de plissage des variétés hyperboliques et ses conséquences.) (French) Zbl 1055.57022
Seminar on spectral theory and geometry. 2002–2003. St. Martin d’Hères: Université de Grenoble I, Institut Fourier. Sémin. Théor. Spectr. Géom. 21, 103-115 (2003).
Given a compact three manifold, this paper gives a characterization of measured geodesic laminations on the boundary which are the pleating laminations of a geometrically finite hyperbolic structure on the interior. This characterization is given in terms of weights of closed leaves and intersection indices with essential discs and annuli; when the boundary is incompressible or the lamination is supported in a finite number of compact leaves, it has been proved by Bonahon and Otal. The proof given here uses the fact that laminations satisfying the conditions are limits of laminations for which Bonahon-Otal’s theorem applies, together with a closeness argument.
Among other applications, the author characterizes the discontinuity domain for the action of the mapping class group of a 3-manifold on the space of measured laminations of its boundary.
For the entire collection see [Zbl 1032.35005].

57M50 General geometric structures on low-dimensional manifolds
30F40 Kleinian groups (aspects of compact Riemann surfaces and uniformization)
30F45 Conformal metrics (hyperbolic, Poincaré, distance functions)
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