Topology of certain quotient spaces of Stiefel manifolds. (English) Zbl 1369.55012

Basu, Samik; Subhash, B.

Can. Math. Bull. 60, No. 2, 235-245 (2017).

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

Keywords:

right generalized projective Stiefel manifolds; spectral sequences