Integrability of Lie brackets
Differential Geometry
2007-05-23 v5 Mathematical Physics
math.MP
Quantum Algebra
Symplectic Geometry
Abstract
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.
Cite
@article{arxiv.math/0105033,
title = {Integrability of Lie brackets},
author = {Marius Crainic and Rui L. Fernandes},
journal= {arXiv preprint arXiv:math/0105033},
year = {2007}
}
Comments
46 pages, published version