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Lie Algebroids, Holonomy and Characteristic Classes

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 prove a Stability Theorem. We also introduce secondary or exotic characteristic classes, thus providing invariants which generalize the modular class of a Lie algebroid.