Abstract:In this talk, we first introduce various models to study what a generic 3-manifold looks like. We then focus on the Heegaard splitting model of 3-manifolds, equipped with geometric complexity using Teichmuller metric. The main result is that the Hempel distance of a generic Heegaard splitting goes linearly to the infinity. In particular, generic 3-manifolds are hyperbolic in this mode...
AbstractIn this lecture, we wil study contractible 3-manifolds and its relationship with positive scalarcurvature. For example, Whitehead manifold is a contractible 3-manifold, but not homomorphic to3-dimensional Euclidean space. We will give a proof that Whitehead manifold does not have a acomplete metric with positive scalar curvature.Lecture 1: We will focus on the construction of contractib...