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Conformal Geometry and Dynamics
Conformal Geometry and Dynamics
ISSN 1088-4173

 

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
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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
Email: gou@aitech.ac.jp

Toshihiro Nakanishi
Affiliation: Department of Mathematics, Shimane University, Matsue, 690-8504, Japan
Email: tosihiro@riko.shimane-u.ac.jp

DOI: http://dx.doi.org/10.1090/S1088-4173-2013-00254-3
PII: S 1088-4173(2013)00254-3
Keywords: Teichm\"uller 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.