Nathan Lopez : An Introduction to Teichmüller Space

Posted by Wes Townsend , part of the Graduate Student Colloquium.

At

Oct. 17, 2016, 1 p.m.

In

SEO 636

Abstract

Consider a surface S of genus g>1 with n\geq 0 punctures. A crucial tool in the study of automorphisms of S is its Teichmüller Space \mathcal{T}(S), i.e., the space of isotopy classes of hyperbolic structures on S. My first goal in this talk is to explain what \mathcal{T}(S) is, examine its topology, and compute a few examples. Secondly, I'll provide some context and motivation for Teichmüller theory by giving a brief survey of the Dehn-Thurston classification and of Thurston's asymmetric metric on \mathcal{T}(S). To cover so much in just an hour, I'll focus less on rigor and more on intuition.