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Integrability of Lie brackets. (English) Zbl 1037.22003

The extension of Lie’s first and second theorems to Lie algebroids is well known – see [C. H. K. Mackenzie and P. Xu, Topology 39, 445–467 (2000; Zbl 0961.58009); V. Nistor, J. Math. Soc. Japan 52, 847–868 (2000; Zbl 0965.58023)] – but in contrast with the Lie algebras, there is no Lie’s third theorem for Lie algebroids. It is shown that the integrability problem is controlled by two computable (longitudinal and transverse) obstructions. As applications, some examples of nonintegrability and integrability are discussed.

MSC:

22A22 Topological groupoids (including differentiable and Lie groupoids)
20-XX Group theory and generalizations
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