TEICHM LLER THEORY OF THEUNIVERSAL HYPERBOLIC LAMINATION

摘要

We construct an Ahlfors-Bers complex analytic model for the Teichmller space of the universal hyperbolic lamination (also known as Sullivan's Teichmller space) and the renormalized Weil-Petersson metric on it as an extension of the usual one. In this setting, we prove that Sullivan's Teichmller space is Khler isometric biholomophic to the space of continuous functions from the profinite completion of the fundamental group of a compact Riemann surface of genus greater than or equal to two to the Teichmller space of this surface; i.e. we find natural Khler coordinates for the Sullivan's Teichmller space. This is the main result. As a corollary we show the expected fact that the Nag-Verjovsky embedding is transversal to the Sullivan's Teichmller space contained in the universal one.