Embedding Coverings in Bundles

http://dx.doi.org/10.4153/CMB-1999-006-8
Canad. Math. Bull. 42(1999), 52-55

  Published:1999-03-01
 Printed: Mar 1999

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 $d'=1$.