2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/127978We will provide a lower bound for the equivariant Lusternik-Schnirelmann category of an arbitrary proper action in terms of the stratification by orbit types, and an upper bound for proper polar actions in terms of the equivariant Lusternik-Schnirelmann category of its generalized Weyl group. As an application we reprove a theorem of Singhof that determines the classical Lusternik-Schnirelmann category for U(n) and SU(n).Differential Geometry55M30; 57S15text