, Volume 11, Issue 1, pp 51-89

Characteristic invariants of foliated bundles

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Abstract

This paper gives a construction of characteristic invariants of foliated principal bundles in the category of smooth and complex manifolds or non-singular algebraic varieties. It contains a generalization of the Chern-Weil theory requiring no use of global connections. This construction leads for foliated bundles automatically to secondary characteristic invariants. The generalized Weil-homomorphism induces a homomorphism of spectral sequences. On the E1-level this gives rise to further characteristic invariants (derived characteristic classes). The new invariants are geometrically interpreted and examples are discussed.