Contractible 3-manifolds and positive scalar curvature (II)

Abstract

In this article, we are interested in the question whether any complete contractible 3- manifold of positive scalar curvature is homeomorphic to ${\mathbb{R}}^3$. We study the fundamental group at infinity, ${\pi }_1^{\infty }$, and its relationship to the existence of complete metrics of positive scalar curvature. We prove that a complete contractible 3-manifold with positive scalar curvature and trivial ${\pi }_1^{\infty }$ 1 is homeomorphic to ${\mathbb{R}}^3$.