Simply connected open 3-manifolds with slow decay of positive scalar curvature

Abstract

The goal of this paper is to investigate the topological structure of open simply connected 3-manifolds whose scalar curvature has a slow decay at infinity. In particular, we show that the Whitehead manifold does not admit a complete metric whose scalar curvature decays slowly, and in fact that any contractible complete 3-manifolds with such a metric is diffeomorphic to R3. Furthermore, using this result, we prove that any open simply connected 3-manifold M with π2(M)=Z and a complete metric as above is diffeomorphic to S2×R.