, 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.

Text of lectures given during the meeting on “Exotic Characteristic Classes” in Lille, February 1973.
This work was partially supported by a grant from the National Science Foundation and by the Forschungsinstitut für Mathematik of the ETH in Zürich.