2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70980The harmonic cohomology of a Donaldson symplectic submanifold and of an Auroux symplectic submanifold are compared with that of its ambient space. We also study symplectic manifolds satisfying a weakly Lefschetz property, that is, the $s$-Lefschetz propery. In particular, we consider the symplectic blow-ups of the complex projective space along weakly Lefschetz symplectic submanifolds. As an application we construct, for each even integer $s\geq 2$, compact symplectic manifolds which are $s$-Lefschetz but not $(s+1)$-Lefschetz.22 pages; many improvements from previous versionSymplectic GeometryDifferential Geometry53D05text