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.
Classification : 55R25, 57R20, 57R22, 57R25
Keywords: CW-complex; oriented vector bundle; characteristic classes; Postnikov tower 
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     author = {\v{C}adek, Martin and Van\v{z}ura, Ji\v{r}{\'\i}},
     title = {On oriented vector bundles over {CW-complexes} of dimension 6 and 7},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {727--736},
     publisher = {mathdoc},
     volume = {33},
     number = {4},
     year = {1992},
     mrnumber = {1240195},
     zbl = {0790.57016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1992__33_4_a18/}
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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/