2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71816Given a Lagrangian submanifold in a symplectic manifold and a Morse function on the submanifold, we show that there is an isotopic Morse function and a symplectic Lefschetz pencil on the manifold extending the Morse function to the whole manifold. From this construction we define a sequence of symplectic invariants classifying the isotopy classes of Lagrangian spheres in a symplectic 4-manifold.40 pages, 1 figureSymplectic GeometryDifferential Geometry53D12; 53D35text