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

 

A quasiconformal mapping class group acting trivially on the asymptotic Teichmüller space


Author: Katsuhiko Matsuzaki
Journal: Proc. Amer. Math. Soc. 135 (2007), 2573-2579
MSC (2000): Primary 30F60; Secondary 32G15
Published electronically: March 22, 2007
MathSciNet review: 2302578
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Abstract: For an analytically infinite Riemann surface $ R$, the quasiconformal mapping class group $ \operatorname{MCG}(R)$ always acts faithfully on the ordinary Teichmüller space $ T(R)$. However in this paper, an example of $ R$ is constructed for which $ \operatorname{MCG}(R)$ acts trivially on its asymptotic Teichmüller space $ AT(R)$.


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Additional Information

Katsuhiko Matsuzaki
Affiliation: Department of Mathematics, Ochanomizu University, Tokyo 112-8610, Japan
Address at time of publication: Department of Mathematics, Okayama University, Okayama 700-8530, Japan
Email: matsuzak@math.okayama-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08761-8
PII: S 0002-9939(07)08761-8
Keywords: Analytically infinite Riemann surface, quasiconformal mapping class group, asymptotic Teichm\"{u}ller space
Received by editor(s): August 16, 2005
Received by editor(s) in revised form: April 19, 2006
Published electronically: March 22, 2007
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.