Lie Algebroids, Holonomy and Characteristic Classes

Details Lie Algebroids, Holonomy and Characteristic Classes Lie Algebroids, Holonomy and Characteristic Classes

2000-07-21

arxiv.org/abs/math/0007132v2

Mathematics

Differential Geometry

Several typos corrected. References added. Final version for publication

Scientific paper

We extend the notion of connection in order to be able 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 connection. Using connections, we are able to define holonomy of the orbit foliation of a Lie algebroid and prove a stability theorem. We also introduce secondary or exotic characteristic classes that generalize the modular class of a Lie algebroid.

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