Necessary and sufficient conditions for the existence of two linearly independent sections in an 8-dimensional spin vector bundle over a CW-complex of the same dimension are given in terms of characteristic classes and a certain secondary cohomology operation. In some cases this operation is computed.
@article{118764, author = {Martin \v Cadek and Ji\v r\'\i\ Van\v zura}, title = {On the existence of 2-fields in 8-dimensional vector bundles over 8-complexes}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {36}, year = {1995}, pages = {377-394}, zbl = {0921.57016}, mrnumber = {1357537}, language = {en}, url = {http://dml.mathdoc.fr/item/118764} }
Čadek, Martin; Vanžura, Jiří. On the existence of 2-fields in 8-dimensional vector bundles over 8-complexes. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) pp. 377-394. http://gdmltest.u-ga.fr/item/118764/
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