# Article

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Keywords:
CW-complex; oriented vector bundle; characteristic classes; Postnikov tower
Summary:
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.
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