On the classification of oriented vector bundles over 9-complexes

Čadek, Martin; Vanžura, Jiří

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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 $\leq 7$ 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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