Semialgebraic Description of Teichmiiller Space

  • Yohei Komori

    Osaka City University, Japan


We give a concrete semialgebraic description of Teichmiiller space of the closed surface group of genus . Our result implies that for any -representation of , we can determine whether this representation is discrete and faithful or not by using explicit trace inequalities. We also show the connectivity and contractibility of from the point of view of -representations of . 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 -representations of .

Cite this article

Yohei Komori, Semialgebraic Description of Teichmiiller Space. Publ. Res. Inst. Math. Sci. 33 (1997), no. 4, pp. 527–571

DOI 10.2977/PRIMS/1195145147