Dissolving four-manifolds and positive scalar curvature

Abstract

We prove that many simply connected symplectic four-manifolds dissolve after connected sum with only one copy of $S^2\times S^2$. For any finite group G that acts freely on the three-sphere we construct closed smooth four-manifolds with fundamental group G which do not admit metrics of positive scalar curvature, but whose universal covers do admit such metrics.

13 pages; to appear in Mathematische Zeitschrift