"The Chern-Weil Homomorphism of regular Lie Algebroids"

REPRINT (habilitation work): UNIVERSITE CLAUDE BERNARD – LYON 1, Publications du Départment de Mathématiques, nouvelle série, 1991, 1-70.
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The aim of this paper is to construct the Chern-Weil homomorphism or regular Lie algebroids. This homomorphism, in the case of an arbitrary integrable transitive Lie algebroid A, agrees with the one for any connected principal bundle for which A is its Lie algebroid. Next, it is proved that there exist nonintegrable transitive Lie algebroids having the nontrivial Chern-Weil homomorphism. Lie algebroids of some transversally complete foliations have this property. Some applications to nonclosed Lie subgroups are given.