Cohomology of Complex Projective Stiefel Manifolds

Abstract

Abstract The cohomology algebra mod p of the complex projective Stiefel manifolds is determined for all primes p . When p = 2 we also determine the action of the Steenrod algebra and apply this to the problem of existence of trivial subbundles of multiples of the canonical line bundle over a lens space with 2-torsion, obtaining optimal results in many cases.