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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the homeomorphisms of the space of geodesic laminations on a hyperbolic surface


Authors: C. Charitos, I. Papadoperakis and A. Papadopoulos
Journal: Proc. Amer. Math. Soc. 142 (2014), 2179-2191
MSC (2010): Primary 57M50; Secondary 20F65, 57R30
Published electronically: March 5, 2014
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Abstract: We prove that for any orientable connected surface $ S$ of finite type which is not a sphere with at most four punctures or a torus with at most two punctures, the natural homomorphism from the extended mapping class group of $ S$ to the group of homeomorphisms of the space of geodesic laminations on $ S$, equipped with the Thurston topology, is an isomorphism.


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Additional Information

C. Charitos
Affiliation: Laboratory of Mathematics, Agricultural University of Athens, Iera Odos 75, 118 55 Athens, Greece
Email: bakis@aua.gr

I. Papadoperakis
Affiliation: Laboratory of Mathematics, Agricultural University of Athens, Iera Odos 75, 118 55 Athens, Greece
Email: papadoperakis@aua.gr

A. Papadopoulos
Affiliation: Institut de Recherche Mathématique Avancée, Université de Strasbourg and CNRS, 7 rue René Descartes, 67084 Strasbourg Cedex, France
Email: athanase.papadopoulos@math.unistra.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-2014-11934-4
PII: S 0002-9939(2014)11934-4
Keywords: Geodesic lamination, mapping class group, hyperbolic surface, Hausdorff topology, Thurston topology
Received by editor(s): December 26, 2011
Received by editor(s) in revised form: July 3, 2012, and July 9, 2012
Published electronically: March 5, 2014
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2014 American Mathematical Society