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Embedding Coverings in Bundles

Published online by Cambridge University Press:  20 November 2018

Allan L. Edmonds
Allan L. Edmonds*
Affiliation:
Department of Mathematics Indiana University Bloomington, IN 47405 USA, email: edmonds@indiana.edu
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Abstract

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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 $d{{d}^{\prime }}\text{e(V)}\text{=}\text{0}$ where ${{d}^{\prime }}$ is a certain divisor of $d\,-\,1$ , and often ${{d}^{\prime }}=1$ .

Keywords

57M1055R2555S4057N35

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 42 , Issue 1 , 01 March 1999, pp. 52 - 55
Copyright
Copyright © Canadian Mathematical Society 1999

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