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

Nakamura, Gou; Nakanishi, Toshihiro

doi:10.1090/ecgd/289

Parametrizations of Teichmüller spaces by trace functions and action of mapping class groups
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by Gou Nakamura and Toshihiro Nakanishi PDF

Conform. Geom. Dyn. 20 (2016), 25-42 Request permission

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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