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Topology of certain quotient spaces of Stiefel manifolds. (English) Zbl 1369.55012
This paper deals with right generalized projective Stiefel manifolds $$\mathcal P_l (W_{n,k})$$ which are obtained as quotients of Stiefel manifolds $$W_{n,k}$$ of orthonormal $$k$$-frames in $$\mathbb C^n$$ by an action of the circle group $$\mathbb S^1$$. They are smooth real manifolds of dimension $$k(2n-k)-1$$.
In this paper the authors compute the cohomology ring of these manifolds using spectral sequences.
Reviewer: Cenap Özel (Bolu)
##### MSC:
 55R20 Spectral sequences and homology of fiber spaces in algebraic topology 55R25 Sphere bundles and vector bundles in algebraic topology
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