Jeff Brock : Entomology and morphology in hyperbolic geometry

Posted by Marc Culler , part of the Departmental Colloquium.

At

April 11, 2014, 3 p.m.

In

SEO 636

Abstract

The classification of hyperbolic 3-manifolds with finitely generated fundamental group involves sorting a lot of pretty ugly looking bugs. Geometrically, this classification reduces to Thurston's <i>Ending Lamination Conjecture</i>; our proof (with Canary and Minsky) produced an array of tools for understanding how a topological specification of a 3-manifold relates to its "shape" or geometry. One such specification, the <i>Heegaard splitting</i>, seems ripe for exploration along these lines, yet a complete picture is still under development. I'll review the state of things, and discuss some key examples.