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Conformal Geometry and Dynamics

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Pure mapping class group acting on Teichmüller space

Author: Ege Fujikawa
Journal: Conform. Geom. Dyn. 12 (2008), 227-239
MSC (2000): Primary 30F60; Secondary 37F30
Published electronically: December 23, 2008
MathSciNet review: 2466018
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Abstract: For a Riemann surface of analytically infinite type, the action of the quasiconformal mapping class group on the Teichmüller space is not discontinuous in general. In this paper, we consider pure mapping classes that fix all topological ends of a Riemann surface and prove that the pure mapping class group acts on the Teichmüller space discontinuously under a certain geometric condition of a Riemann surface. We also consider the action of the quasiconformal mapping class group on the asymptotic Teichmüller space. Non-trivial mapping classes can act on the asymptotic Teichmüller space trivially. We prove that all such mapping classes are contained in the pure mapping class group.

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Additional Information

Ege Fujikawa
Affiliation: Department of Mathematics, Chiba University, 1-33 Yayoi-cho, Inage, Chiba, 263-8522, Japan

Keywords: Riemann surface of infinite type, quasiconformal mapping class group, asymptotic Teichm\"uller space, hyperbolic geometry
Received by editor(s): May 19, 2008
Published electronically: December 23, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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