2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60391We use Liu-Tian's virtual moduli cycle methods to construct detailedly the explicit isomorphism between Floer homology and quantum homology for any closed symplectic manifold that was first outlined by Piunikhin, Salamon and Schwarz for the case of the semi-positive symplectic manifolds.Latex, published versionDifferential GeometryGeometric TopologySymplectic Geometry53CR15; 58F05; 58E05; 57R57text