The cohomology rings of real Stiefel manifolds with integer coefficients (Q1890284)

This paper determines the ring structure of the integral cohomology \(H^{*}(V_{n,k};{\mathbb Z})\) of the Stiefel manifold of \(k\)-planes in \(n\)-space. The methods, which use induction and the Gysin sequence, are independent of those of \textit{H. V. Pittie} [J. Pure Appl. Algebra 73, No. 2, 105--153 (1991; Zbl 0736.57019)].