Dissolving four-manifolds and positive scalar curvature

Hanke, B.; Kotschick, D.; Wehrheim, J.

Dissolving four-manifolds and positive scalar curvature

Authors

Hanke, B.

Kotschick, D.

Wehrheim, J.

Description

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