2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67704We 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 ZeitschriftGeometric TopologyDifferential GeometrySymplectic Geometry57R57; 53C25; 57R55text