Lie algebroids, holonomy and characteristic classes. (English) Zbl 1007.22007

Fernandes, Rui Loja

Adv. Math. 170, No. 1, 119-179 (2002).

From the author’s abstract: “We extend the notion of connection in order to study singular geometric structures, namely, we consider a notion of connection on a Lie algebroid which is a natural extension of the usual concept of a covariant connection. It allows us to define holonomy of the orbit foliation of a Lie algebroid and to prove a stability theorem. We also introduce secondary or exotic characteristic classes, thus providing invariants which generalize the modular class of a Lie algebroid”.

Reviewer: Vladislav Goldberg (Newark)

MSC:

22A22	Topological groupoids (including differentiable and Lie groupoids)
53C07	Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)
17B99	Lie algebras and Lie superalgebras

Keywords:

Lie algebroid; connection; holonomy; characteristic

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