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Parametrizations of Teichmüller spaces by trace functions and action of mapping class groups


Authors: Gou Nakamura and Toshihiro Nakanishi
Journal: Conform. Geom. Dyn. 20 (2016), 25-42
MSC (2010): Primary 32G15; Secondary 30F35
DOI: https://doi.org/10.1090/ecgd/289
Published electronically: March 18, 2016
MathSciNet review: 3475293
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Abstract: We give a set of trace functions which give a global parametrization of the Teichmüller space $ \mathcal {T}(g,n)(L_1,\dots ,L_n)$ of hyperbolic surfaces of genus $ g$ with $ n$ geodesic boundary components of lengths $ L_1$,..., $ L_n$ such that the action of the mapping class group on the Teichmüller space can be represented by rational transformations in the parameters.


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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: https://doi.org/10.1090/ecgd/289
Received by editor(s): July 2, 2015
Received by editor(s) in revised form: January 11, 2016
Published electronically: March 18, 2016
Additional Notes: The first author was partially supported by the JSPS KAKENHI Grant No. 25400147.
The second author was partially supported by the JSPS KAKENHI Grant No. 22540191.
Dedicated: Dedicated to the memory of Professor Mika Seppälä
Article copyright: © Copyright 2016 American Mathematical Society