Hyperbolicity of the Arc and Curve Complex

Geometry Topology Student Seminar
Wednesday, February 13, 2013 - 13:00
1 hour (actually 50 minutes)
Skiles 005
Georgia Tech
Given any surface, we can construct its curve complex by considering isotopy classes of curves on the surface.  If the surface has boundary, we can construct its arc complex similarly, with isotopy clasess of arcs, with endpoints on the boundary.  In 1999, Masur and Minsky proved that these complexes are hyperbolic, but the proof is long and involved.  This talk will discuss a short proof of the hyperbolicity of the curve and arc complex recently given by Hensel, Przytycki, and Webb.