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L’extension du flot de Fenchel-Nielsen au bord de Thurston de l’espace de Teichmüller. (The extension of the Fenchel-Nielsen flow on Thurston’s boundary of Teichmüller space). (French) Zbl 0598.57016

The author has studied in a previous paper [Pac. J. Math. 124, 375-402 (1986)] a flow on the space of measured foliations on a surface. This flow on \({\mathcal M}{\mathcal F}\) is an analogue of the classical Fenchel- Nielsen flow on the Teichmüller space and associated to a nontrivial circle on the surface in question. In the paper the author proves that a suitable reparametrization of the Fenchel-Nielsen flow extends to the Thurston boundary \({\mathcal P}{\mathcal M}{\mathcal F}\) of the Teichmüller space and that this extension is equal to the quotient of the flow on \({\mathcal M}{\mathcal F}\) (recall that \({\mathcal P}{\mathcal M}{\mathcal F}={\mathcal M}{\mathcal F}\setminus 0/{\mathbb{R}}_+)\). This result was inspired by an (unpublished) theorem due to S. P. Kerchkoff. According to this theorem the Fenchel- Nielsen flow itself extends to the identity on \({\mathcal P}{\mathcal M}{\mathcal F}\).
Reviewer: N.V.Ivanov

MSC:

57R30 Foliations in differential topology; geometric theory
57N05 Topology of the Euclidean \(2\)-space, \(2\)-manifolds (MSC2010)
32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)
57R50 Differential topological aspects of diffeomorphisms
37-XX Dynamical systems and ergodic theory