Lie algebroid fibrations (Q626105)

This paper introduces a notion of fibration for Lie algebroids. Let us recall that fibrations for Lie algebroids are very usefull since Lie algebroids are a central physical concept. In this work, the authors first prove the existence of a complete Ehresmann connection. Then, they define homotopy groups and prove that a Lie algebroid fibration corresponds to a Kan fibration of the associated simplicial objects. Finally, the authors show how their results can be applied to better understand Crainic and Fernandes's obstruction to the integrability of Lie algebroids.