Cohomology of Complex Projective Stiefel Manifolds

http://dx.doi.org/10.4153/CJM-1999-039-2
Canad. J. Math. 51(1999), 897-914

  Published:1999-10-01
 Printed: Oct 1999

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.