On 4-fields and 4-distributions in 8-dimensional vector bundles over 8-complexes

Volume 76 / 1998

Martin Čadek, Jiří Vanžura Colloquium Mathematicum 76 (1998), 213-228 DOI: 10.4064/cm-76-2-213-228

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.

Authors

  • Martin Čadek
  • Jiří Vanžura

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