Geodesic
On oriented vector bundles over CW-complexes of dimension 6 and 7
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 4, pp. 727-736
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Necessary and sufficient conditions for the existence of $n$-dimensional oriented vector bundles ($n=3,4,5$) over CW-complexes of dimension $\le 7$ with prescribed Stiefel-Whitney classes $w_2=0$, $w_4 $ and Pontrjagin class $p_1$ are found. As a consequence some results on the span of 6 and 7-dimensional oriented vector bundles are given in terms of characteristic classes.
Necessary and sufficient conditions for the existence of $n$-dimensional oriented vector bundles ($n=3,4,5$) over CW-complexes of dimension $\le 7$ with prescribed Stiefel-Whitney classes $w_2=0$, $w_4 $ and Pontrjagin class $p_1$ are found. As a consequence some results on the span of 6 and 7-dimensional oriented vector bundles are given in terms of characteristic classes.
Classification : 55R25, 57R20, 57R22, 57R25
Keywords: CW-complex; oriented vector bundle; characteristic classes; Postnikov tower 
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Čadek, Martin; Vanžura, Jiří. On oriented vector bundles over CW-complexes of dimension 6 and 7. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 4, pp. 727-736. http://geodesic.mathdoc.fr/item/CMUC_1992_33_4_a18/

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