Embedding Coverings in Bundles

Abstract

AbstractIfV→Xis a vector bundle of fiber dimensionkandY→Xis a finite sheeted covering map of degreed, the implications for the Euler class e(V) inHk(X)ofVimplied by the existence of an embeddingY→Vlifting 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.