ArticleOriginal scientific text
Title
On 4-fields and 4-distributions in 8-dimensional vector bundles over 8-complexes
Authors 1, 2
Affiliations
- Department of Algebra and Geometry, Masaryk University, Janáčkovo nám. 2a, 662 95 Brno, Czech Republic
- Institute of Mathematics, Academy of Sciences of the Czech Republic, Žižkova 22, 616 62 Brno, Czech Republic
Abstract
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.
Keywords
classifying spaces for groups, vector bundle, higher order cohomology operations, characteristic classes, Postnikov tower, distribution
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