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We give a set of trace functions which give a global parametrization of the Teichmüller space T (g, n)(L1, . . . , Ln) of hyperbolic surfaces of genus g with n geodesic boundary components of lengths L1,. . . , Ln such that the action of the mapping class group on the Teichmüller space can be represented by rational transformations in the parameters.

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