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Conformal Geometry and Dynamics

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Parametrizations of some Teichmüller spaces by trace functions

Authors: Gou Nakamura and Toshihiro Nakanishi
Journal: Conform. Geom. Dyn. 17 (2013), 47-57
MSC (2010): Primary 32G15; Secondary 30F35
Published electronically: April 2, 2013
MathSciNet review: 3037875
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Abstract: We show a tuple of trace functions which give a global parametrization of the Teichmüller space ${\mathcal T}(g,m)$ of types $(1,2)$ and $(2,0)$. We also show that the mapping class group acting on these Teichmüller spaces can be represented by a group of rational transformations in seven variables.

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Additional Information

Gou Nakamura
Affiliation: Science Division, Center for General Education, Aichi Institute of Technology, 1247 Yachigusa, Yakusa, Toyota, 470-0392, Japan
MR Author ID: 639802

Toshihiro Nakanishi
Affiliation: Department of Mathematics, Shimane University, Matsue, 690-8504, Japan
MR Author ID: 225488

Keywords: Teichmüller space, Fuchsian groups
Received by editor(s): June 16, 2011
Published electronically: April 2, 2013
Additional Notes: The first author was partially supported by Grant-in-Aid for Young Scientists (B) (No. 20740081), Japan Society for the Promotion of Science.
The second author was partially supported by Grand-in-Aid for Scientific Research (No. 18540179), Ministry of Education, Science and Culture of Japan.
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.