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Abstract
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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.
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Keywords
Teichmüller space, hyperbolic surface, hyperbolic
structure, geodesic lamination, stretch line, Thurston's
boundary, measured foliation
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Mathematical Subject Classification 2000
Primary: 30F60, 57M50, 53C22
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Publication
Received: 24 April 2010
Revised: 30 June 2010
Accepted: 29 July 2010
Published: 19 December 2010
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