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On the existence of 2-fields in 8-dimensional vector bundles over 8-complexes. (English) Zbl 0921.57016

Summary: 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.

MSC:

57R22 Topology of vector bundles and fiber bundles
55R25 Sphere bundles and vector bundles in algebraic topology
57R25 Vector fields, frame fields in differential topology
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