Integrability of Lie brackets

Details Integrability of Lie brackets Integrability of Lie brackets

2001-05-04

arxiv.org/abs/math/0105033v5

Ann. of Math. (2), Vol. 157 (2003), no. 2, 575--620

Mathematics

Differential Geometry

46 pages, published version

Scientific paper

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.

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