On the Lusternik-Schnirelmann category of Stiefel manifolds (Q881464)

Following the computational method initiated by W. Singhof, the author determines the Lusternik-Schnirelmann category of the real Stiefel manifold \(V_{n,k}\) and of the quaternionic Stiefel manifold \(X_{n,k}\). More precisely, he proves that for \(n\geq 2k\) the Lusternik-Schnirelmann category of \(V_{n,k}\) (respectively of \(X_{n,k}\)) equals the cup-length of \(H^*(V_{n,k};\mathbb{F}_2)\) (respectively, of \(H^*(X_{n,k};\mathbb{Z}))\).