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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
MR Author ID: 294335
ORCID: 0000-0003-0025-5372

Keywords: Analytically infinite Riemann surface, quasiconformal mapping class group, asymptotic Teichmüller 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.