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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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