LGRT 1685
This week we will discuss the Teichmüller space of a compact surface, following Exposé 7 of Thurston's Work on Surfaces. We will focus on the two main theorems; first, the Teichmüller space of any compact closed surface S of genus >= 2 is homeomorphic to R^(6g-6). Second, the map that sends an element in the Teichmuller space, a curvature -1 hyperbolic metric on S, to the corresponding lengths of 9g-9 simple closed curves is a homeomorphism onto its image.