Abstract

In 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 contractible 3-manifold and its topological propertiesParticularly, we will describe the topology at infinity of contractible 3-manifolds and its relationshipwith knot theory.

Lecture 2: We will study the existence of positive scalar curvature metric on contractible 3-manifold.

Especially, we will talk about how positive scalar curvature effects the topology at infinity.