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Search: MSC category 55R25 ( Sphere bundles and vector bundles )

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1. CMB Online first

Basu, Samik; Subhash, B
Topology of certain quotient spaces of Stiefel manifolds
We compute the cohomology of the right generalised projective Stiefel manifolds. Following this, we discuss some easy applications of the computations to the ranks of complementary bundles, and bounds on the span and immersibility.

Keywords:projective Stiefel manifold, span, spectral sequence
Categories:55R20, 55R25, 57R20

2. CMB 1999 (vol 42 pp. 52)

Edmonds, Allan L.
Embedding Coverings in Bundles
If $V\to X$ is a vector bundle of fiber dimension $k$ and $Y\to X$ is a finite sheeted covering map of degree $d$, the implications for the Euler class $e(V)$ in $H^k(X)$ of $V$ implied by the existence of an embedding $Y\to V$ lifting the covering map are explored. In particular it is proved that $dd'e(V)=0$ where $d'$ is a certain divisor of $d-1$, and often $d'=1$.

Categories:57M10, 55R25, 55S40, 57N35

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