# Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

## On 2-distributions in 8-dimensional vector bundles over 8-complexes

### Tom 70 / 1996

Colloquium Mathematicum 70 (1996), 25-40 DOI: 10.4064/cm-70-1-25-40

#### Streszczenie

It is shown that the $ℤ_2$-index of a 2-distribution in an 8-dimensional spin vector bundle over an 8-complex is independent of the 2-distribution. Necessary and sufficient conditions for the existence of 2-distributions in such vector bundles are given in terms of characteristic classes and a certain secondary cohomology operation. In some cases this operation is computed.