Geodesic
On the existence of 2-fields in 8-dimensional vector bundles over 8-complexes
Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 2, pp. 377-394.

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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.
Classification : 55R25, 57R22, 57R25
Keywords: span of the vector bundle; classifying spaces for spinor groups; characteristic classes; Postnikov tower; secondary cohomology operation 
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     author = {\v{C}adek, Martin and Van\v{z}ura, Ji\v{r}{\'\i}},
     title = {On the existence of 2-fields in 8-dimensional vector bundles over 8-complexes},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {377--394},
     publisher = {mathdoc},
     volume = {36},
     number = {2},
     year = {1995},
     mrnumber = {1357537},
     zbl = {0921.57016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1995__36_2_a15/}
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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) no. 2, pp. 377-394. http://geodesic.mathdoc.fr/item/CMUC_1995__36_2_a15/