Divergence et parallélisme des rayons d’étirement cylindriques

Théret, Guillaume

doi:10.2140/agt.2010.10.2451

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Divergence et parallélisme des rayons d'étirement cylindriques

Guillaume Théret

Algebraic & Geometric Topology 10 (2010) 2451–2468

DOI: 10.2140/agt.2010.10.2451

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

Volume 10, issue 4 (2010)