# Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

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

### Tom 76 / 1998

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

#### Streszczenie

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.