On the homeomorphisms of the space of geodesic laminations on a hyperbolic surface
HTML articles powered by AMS MathViewer
- by C. Charitos, I. Papadoperakis and A. Papadopoulos PDF
- Proc. Amer. Math. Soc. 142 (2014), 2179-2191 Request permission
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.References
- Herbert Busemann, The geometry of geodesics, Academic Press, Inc., New York, N.Y., 1955. MR 0075623
- R. D. Canary, D. B. A. Epstein, and P. L. Green, Notes on notes of Thurston [MR0903850], Fundamentals of hyperbolic geometry: selected expositions, London Math. Soc. Lecture Note Ser., vol. 328, Cambridge Univ. Press, Cambridge, 2006, pp. 1–115. With a new foreword by Canary. MR 2235710
- Andrew J. Casson and Steven A. Bleiler, Automorphisms of surfaces after Nielsen and Thurston, London Mathematical Society Student Texts, vol. 9, Cambridge University Press, Cambridge, 1988. MR 964685, DOI 10.1017/CBO9780511623912
- N. V. Ivanov, Automorphisms of Teichmüller modular groups, Topology and geometry—Rohlin Seminar, Lecture Notes in Math., vol. 1346, Springer, Berlin, 1988, pp. 199–270. MR 970079, DOI 10.1007/BFb0082778
- Mustafa Korkmaz, Automorphisms of complexes of curves on punctured spheres and on punctured tori, Topology Appl. 95 (1999), no. 2, 85–111. MR 1696431, DOI 10.1016/S0166-8641(97)00278-2
- Feng Luo, Automorphisms of the complex of curves, Topology 39 (2000), no. 2, 283–298. MR 1722024, DOI 10.1016/S0040-9383(99)00008-7
- Katsuhiko Matsuzaki and Masahiko Taniguchi, Hyperbolic manifolds and Kleinian groups, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1998. Oxford Science Publications. MR 1638795
- K. Ohshika, Reduced Bers boundaries of Teichmüller spaces, to appear in Ann. Inst. Fourier.
- Ken’ichi Ohshika, A note on the rigidity of unmeasured lamination spaces, Proc. Amer. Math. Soc. 141 (2013), no. 12, 4385–4389. MR 3105880, DOI 10.1090/S0002-9939-2013-11670-9
- Jean-Pierre Otal, Le théorème d’hyperbolisation pour les variétés fibrées de dimension 3, Astérisque 235 (1996), x+159 (French, with French summary). MR 1402300
- Athanase Papadopoulos, A rigidity theorem for the mapping class group action on the space of unmeasured foliations on a surface, Proc. Amer. Math. Soc. 136 (2008), no. 12, 4453–4460. MR 2431062, DOI 10.1090/S0002-9939-08-09433-1
- W. Thurston, The geometry and topology of three manifolds, Princeton Lecture Notes, 1979.
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
- MR Author ID: 135835
- Email: athanase.papadopoulos@math.unistra.fr
- 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
- © Copyright 2014 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 142 (2014), 2179-2191
- MSC (2010): Primary 57M50; Secondary 20F65, 57R30
- DOI: https://doi.org/10.1090/S0002-9939-2014-11934-4
- MathSciNet review: 3182035