Pure mapping class group acting on Teichmüller space
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- by Ege Fujikawa
- Conform. Geom. Dyn. 12 (2008), 227-239
- DOI: https://doi.org/10.1090/S1088-4173-08-00188-4
- Published electronically: December 23, 2008
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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.References
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Bibliographic Information
- Ege Fujikawa
- Affiliation: Department of Mathematics, Chiba University, 1-33 Yayoi-cho, Inage, Chiba, 263-8522, Japan
- MR Author ID: 706593
- Email: fujikawa@math.s.chiba-u.ac.jp
- Received by editor(s): May 19, 2008
- Published electronically: December 23, 2008
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Conform. Geom. Dyn. 12 (2008), 227-239
- MSC (2000): Primary 30F60; Secondary 37F30
- DOI: https://doi.org/10.1090/S1088-4173-08-00188-4
- MathSciNet review: 2466018