Jonah Gaster : Thurston's Skinning Map

Posted by Paul Reschke , part of the Graduate Student Colloquium.

At

April 23, 2012, 4:15 p.m.

In

SEO 636

Abstract

In his Geometrization Theorem for Haken 3-Manifolds, Thurston showed that the study of Riemann surfaces could be used powerfully towards understanding hyperbolic 3-manifolds. We will introduce some of the classical aspects (Teichmuller theory, quasi-Fuchsian space, Ahlfors-Bers correspondences), and then discuss Thurston's skinning map. Given an open hyperbolic 3-manifold, with Riemann surface boundary, one can use the classical theory to 'reflect' the geometry on the boundary at infinity through the 3-manifold, and make sense of what comes out the other side. After a brief survey of relevant results, we will describe an example (work in progress) that seems to indicate that the skinning map can have a critical point. Though all are welcome to attend, this talk is intended to be accessible for graduate students of all levels; no background knowledge of Teichmuller theory is expected.