"Characteristic homomorphisms of regular Lie algebroids"

Poster, European Congress of Mathematics, Paris, July 6-10, 1992.
poster dvi poster ps publications

Differential Geometry has discovered many objects which determine a Lie algebroid [fulfilling a role analogous to that of Lie algebras for Lie groups] as, for example, differential groupoids (and, in consequence, principal bundles) (J.Pradines 1967), transversally complete foliations (and, in consequence, nonclosed Lie subgroups) (P.Molino 1977), Poisson manifolds (A.Coste, P.Dazord, A.Weinstein 1987), and some complete closed pseudogroups (A.Silva 1988). The author has constructed characteristic homomorphisms for regular Lie algebroids:
(a) the Chern-Weil homomorphism,
(b) the characteristic homomorphisms of flat (and partially flat) regular Lie algebroids.
These homomorphisms for integrable Lie algebroids (i.e. transitive ones coming from connected principal bundles) agree with the classical ones of these bundles.
The poster specify 17 sources of Lie algebroids, between them, there is a new source of the so-called S-bundles over foliated manifolds. More details can be founded in the next papers [20], [29], [39].