The equivariant LS-category of polar actions

We will provide a lower bound for arbitrary proper actions in terms of the stratification by orbit types, and an upper bound for proper polar actions in terms of the equivariant LS-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).