Geodesic
Embedding Coverings in Bundles
Canadian mathematical bulletin, Tome 42 (1999) no. 1, pp. 52-55

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DOI

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 ${{d}^{\prime }}=1$ .
DOI : 10.4153/CMB-1999-006-8
Mots-clés : 57M10, 55R25, 55S40, 57N35 
Edmonds, Allan L. Embedding Coverings in Bundles. Canadian mathematical bulletin, Tome 42 (1999) no. 1, pp. 52-55. doi: 10.4153/CMB-1999-006-8
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     title = {Embedding {Coverings} in {Bundles}},
     journal = {Canadian mathematical bulletin},
     pages = {52--55},
     year = {1999},
     volume = {42},
     number = {1},
     doi = {10.4153/CMB-1999-006-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1999-006-8/}
}
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