Let ξ be an oriented 8-dimensional spin vector bundle over an 8-complex. In this paper we give necessary and sufficient conditions for ξ to have 4 linearly independent sections or to be a sum of two 4-dimensional spin vector bundles, in terms of characteristic classes and higher order cohomology operations. On closed connected spin smooth 8-manifolds these operations can be computed.
@article{bwmeta1.element.bwnjournal-article-cmv76z2p213bwm,
author = {Martin \v Cadek and Ji\v r\'\i\ Van\v zura},
title = {On 4-fields and 4-distributions in 8-dimensional vector bundles over 8-complexes},
journal = {Colloquium Mathematicae},
volume = {78},
year = {1998},
pages = {213-228},
zbl = {0894.57021},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv76z2p213bwm}
}
Čadek, Martin; Vanžura, Jiří. On 4-fields and 4-distributions in 8-dimensional vector bundles over 8-complexes. Colloquium Mathematicae, Tome 78 (1998) pp. 213-228. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv76z2p213bwm/
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