2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/105031Our main result offers a new (quite systematic) way of deriving bounds for the cup-length of Poincare spaces over fields; we outline a general research program based on this result. For the oriented Grassmann manifolds, already a limited realization of the program leads, in many cases, to the exact values of the cup-length and to interesting information on the Lyusternik-Shnirel'man category.12 pagesAlgebraic TopologyDifferential Geometry57N65; 55M30 (Primary) 53C30 (Secondary)text