Laminations on the Circle and Cannon's Conjecture

Harry Baik (Cornell)

Abstract: We will see that laminations can be used to study groups acting on the circle. In particular, it is possible to characterize Fuchsian groups in terms of topological invariant laminations. It is a geometrization result in the sense that you start with a topological dynamical data and hyperbolic geometry comes out of the picture. Main motivation of this program is Thurston's universal circle theory for tautly foliated 3-manifolds. We will also discuss how this program is connected to Cannon's conjecture.