Contractible 3-manifold 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 with the existence of complete metrics of positive scalar curvature. We prove that a complete contractible $3$-manifold with positive scalar curvature and trivial ${\pi }_1^{\infty }$ is homeomorphic to ${\mathbb{R}}^3$.

arXiv comment38 Pages, 7 Figures. Accepted by JEMS