Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 41, 2016, 867-879

THURSTON'S METRIC ON TEICHMÜLLER SPACE AND THE TRANSLATION DISTANCES OF MAPPING CLASSES

Athanase Papadopoulos and Weixu Su

Université de Strasbourg and CNRS, Institut de Recherche Mathématique Avancée
7 rue René Descartes, 67084 Strasbourg Cedex, France; athanase.papadopoulos 'at' math.unistra.fr

Fudan University, School of Mathematics
200433, Shanghai, P.R. China; suwx 'at' fudan.edu.cn

Abstract. We show that the Teichmüller space of a surface without boundary and with punctures, equipped with the Thurston metric, is the limit in an appropriate sense of Teichmüller spaces of surfaces with boundary, equipped with their arc metrics, when the boundary lengths tend to zero. We use this to obtain a result on the translation distances of mapping classes for their actions on Teichmüller spaces equipped with the Thurston metric.

2010 Mathematics Subject Classification: Primary 32G15, 30F60.

Key words: Teichmüller space, hyperbolic geometry, quasiconformal mapping, Thurston metric, arc metric, translation distance, mapping class group, pseudo-Anosov, reducible.

Reference to this article: A. Papadopoulos and W. Su: Thurston's metric on Teichmüller space and the translation distances of mapping classes. Ann. Acad. Sci. Fenn. Math. 41 (2016), 867-879.

Full document as PDF file

doi:10.5186/aasfm.2016.4158