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Embedding Coverings in Bundles

 Printed: Mar 1999
  • Allan L. Edmonds
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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 $d'=1$.
MSC Classifications: 57M10, 55R25, 55S40, 57N35 show english descriptions Covering spaces
Sphere bundles and vector bundles
Sectioning fiber spaces and bundles
Embeddings and immersions
57M10 - Covering spaces
55R25 - Sphere bundles and vector bundles
55S40 - Sectioning fiber spaces and bundles
57N35 - Embeddings and immersions

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