# Integrability of Lie brackets

@article{Crainic2001IntegrabilityOL, title={Integrability of Lie brackets}, author={Marius Crainic and Rui Loja Fernandes}, journal={Journal of Differential Equations}, year={2001} }

In this paper we present the solution to a longstanding problem of differential geometry: Lie’s third theorem for Lie algebroids. We show that the integrability problem is controlled by two computable obstructions. As applications we derive, explain and improve the known integrability results, we establish integrability by local Lie groupoids, we clarify the smoothness of the Poisson sigma-model for Poisson manifolds, and we describe other geometrical applications.

## 340 Citations

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