2018/02/16 by Burgos, Juan Manuel, Verjovsky, Alberto
#32G05 #32G15 #32G81 #57R30 #Complex Variables (math.CV) #FOS: Mathematics #Secondary: 22C05
paper · doi:10.48550/arxiv.1802.05830
We construct an Ahlfors-Bers complex analytic model for the Teichmüller space of the universal hyperbolic lamination (also known as Sullivan's Teichmüller space) and the renormalized Weil-Petersson metric on it as an extension of the usual one. In this setting, we prove that Sullivan's Teichmüller space is Kähler isometric biholomorphic 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 Teichmüller space of this surface; i.e. We find natural Kähler coordinates for the Sullivan's Teichmüller 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 Teichmüller space contained in the universal one.