EVENT DETAILS AND ABSTRACT

Title: Surface subgroups from linear programming
Speaker: Danny Calegari
Speaker Info: University of Chicago
Brief Description:
Special Note: Please not the unusual time and place.
Abstract:

A famous question of Gromov asks whether every (one-ended) hyperbolic group contains a subgroup which is isomorphic to the fundamental group of a closed surface. Surface subgroups play a very important role in many areas of low-dimensional topology, for example in Agol's recent resolution of the virtual Haken conjecture. I would like to describe several ways to build surface subgroups in certain hyperbolic groups. The role of hyperbolicity is twofold here: first, hyperbolic geometry allows one to certify injectivity by *local* data; second, hyperbolic dynamics allows one to use ergodic theory to produce the pieces out of which an injective surface can be built. I would like to sketch a proof of the fact that an HNN extension of a free group associated to a ''random'' endomorphism contains a surface subgroup with probability one. This is joint work with Alden Walker.