Çağlar Uyanik (UW-Madison): Surfaces in hyperbolic 3-manifolds and boundary maps

Abstract: A celebrated theorem of Thurston asserts that a 3-manifold that fibers over the circle with fibers closed hyperbolic surfaces admit a hyperbolic metric if and only if the monodromy is pseudo-Anosov. The surface subgroup is exponentially distorted in the 3-manifold group. I will talk about how this distortion manifests itself by looking at the induced map on the boundary at infinities.