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Divergence et parallélisme des rayons d'étirement cylindriques

Guillaume Théret

Algebraic & Geometric Topology 10 (2010) 2451–2468
Abstract

Une ligne d’étirement cylindrique est une ligne d’étirement au sens de Thurston dont la lamination horocyclique est une multicourbe pondérée. Nous montrons ici que deux lignes cylindriques correctement paramétrées sont parallèles si et seulement si ces lignes convergent vers le même point du bord de Thurston de l’espace de Teichmüller.

A cylindrical stretch line is a stretch line, in the sense of Thurston, whose horocyclic lamination is a weighted multicurve. In this paper, we show that two correctly parameterized cylindrical lines are parallel if and only if these lines converge towards the same point in Thurston’s boundary of Teichmüller space.

Keywords
Teichmüller space, hyperbolic surface, hyperbolic structure, geodesic lamination, stretch line, Thurston's boundary, measured foliation
Mathematical Subject Classification 2000
Primary: 30F60, 57M50, 53C22
References
Publication
Received: 24 April 2010
Revised: 30 June 2010
Accepted: 29 July 2010
Published: 19 December 2010
Authors
Guillaume Théret
Max Planck Institut für Mathematik
Vivatsgasse 7
53100 Bonn
Germany