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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Thurston's weak metric on the Teichmüller space of the torus


Authors: Abdelhadi Belkhirat, Athanase Papadopoulos and Marc Troyanov
Journal: Trans. Amer. Math. Soc. 357 (2005), 3311-3324
MSC (2000): Primary 30F60, 32G15
Published electronically: February 4, 2005
MathSciNet review: 2135749
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Abstract: We define and study a natural weak metric on the Teichmüller space of the torus. A similar metric has been defined by W. Thurston on the Teichmüller space of higher genus surfaces and our definition is motivated by Thurston's definition. However, we shall see that in the case of the torus, this metric has a different behaviour than on higher genus surfaces.


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Additional Information

Abdelhadi Belkhirat
Affiliation: Département de Recherche Mathématique Avancée, Université Louis Pasteur and CNRS, 7 rue René Descartes, 67084 Strasbourg Cedex, France
Address at time of publication: King Fahd University of Petroleum and Minerals, Hail Community College, P.O. Box 2440, Hail, Saudi Arabia
Email: belkhirat@math.u-strasbg.fr, belkhirat@hcc.kfupm.edu.sa

Athanase Papadopoulos
Affiliation: Département de Recherche Mathématique Avancée, Université Louis Pasteur and CNRS, 7 rue René Descartes, 67084 Strasbourg Cedex, France
Email: papadopoulos@math.u-strasbg.fr

Marc Troyanov
Affiliation: Section de Mathématiques, École Polytechnique Féderale de Lausanne, 1015 Lausanne, Switzerland
Email: marc.troyanov@epfl.ch

DOI: http://dx.doi.org/10.1090/S0002-9947-05-03735-9
PII: S 0002-9947(05)03735-9
Keywords: Teichm\"uller space, Teichm\"uller metric, Thurston metric, nonsymmetric metric, weak metric, hyperbolic plane, quasi-isometry
Received by editor(s): February 3, 2004
Published electronically: February 4, 2005
Article copyright: © Copyright 2005 American Mathematical Society