Parametrizations of some Teichmüller spaces by trace functions

Nakamura, Gou; Nakanishi, Toshihiro

doi:10.1090/S1088-4173-2013-00254-3

Parametrizations of some Teichmüller spaces by trace functions
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by Gou Nakamura and Toshihiro Nakanishi

Conform. Geom. Dyn. 17 (2013), 47-57

DOI: https://doi.org/10.1090/S1088-4173-2013-00254-3

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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