Topology of certain quotient spaces of stiefel manifolds

TL;DR

This paper computes the cohomology of specific quotient spaces of Stiefel manifolds to derive bounds on vector bundle ranks, span, and immersibility, advancing understanding of their topological properties.

Contribution

It introduces new cohomology computations for generalized projective Stiefel manifolds and applies these to bounds on vector bundle ranks and manifold immersibility.

Findings

Bounds on the rank of the complementary bundle are established.

Constraints on the span of the manifolds are derived.

Results on the immersibility of the manifolds are obtained.

Abstract

We compute the cohomology of the right generalised projective Stiefel manifolds and use it to find bounds on the rank of the complementary bundle for certain vector bundles. Further the cohomology computations are also used to find bounds on the span and on the immersibility of the manifolds in certain cases.