SMOOTH CONNECTIONS AND HORIZONTAL DISTRIBUTIONS
ON MANIFOLDS  OVER LOCAL ALGEBRAS

V.V.Shurygin

Key words: Foliation, manifold over algebra,
           $d_F$-cohomology, $(X,G)$-foliation

1991 Math. Subject Classification: 53C05, 53C12, 57R30, 58A20.

Abstract: On manifolds over local algebras special distributions
     complementary to leaves of the canonical foliation and smooth
     connections are considered. The main purpose is to study
     obstructions to existence of such distributions in terms of
     the Atiyah classes of foliated and smooth principal bundles.
     Besides that the notion of holonomy of a manifold
     over local algebra is introduced, and it is shown that existence of
     complementary distributions under consideration on a manifold
     over local algebra depends on its holonomy.