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# Cohomology of Complex Projective Stiefel Manifolds

Published:1999-10-01
Printed: Oct 1999
• L. Astey
• S. Gitler
• E. Micha
• G. Pastor
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## 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.
 MSC Classifications: 55N10 - Singular theory 55S10 - Steenrod algebra