We give a concrete semialgebraic description of Teichmüller space Tg of the closed surface group Γg of genus g(≥2). Our result implies that for any SL2(R)-representation of Γg, we can determine whether this representation is discrete and faithful or not by using 4g-6 explicit trace inequalities. We also show the connectivity and contractibility of Tg from the point of view of SL2(R)-representations of Γg. Previously, these properties of Tg had been proved by using hyperbolic geometry and quasi-conformal deformations of Fuchsian groups. Our method is simple and only uses topological properties of the space of SL2(R)-representations of Γg.
|ジャーナル||Publications of the Research Institute for Mathematical Sciences|
|出版物ステータス||Published - 1997 12|
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