On the integration of Poisson manifolds, Lie algebroids, and coisotropic submanifolds

Details On the integration of Poisson manifolds, Lie algebroids, and coisotropic submanifolds On the integration of Poisson manifolds, Lie algebroids, and coisotropic submanifolds

2003-08-19

arxiv.org/abs/math/0308180v2

Lett. Math. Phys. 67, 33-48 (2004)

Mathematics

Symplectic Geometry

17 pages. Replacement: 18 pages, minor corrections, references added. To appear in Lett. Math. Phys

Scientific paper

In recent years methods for the integration of Poisson manifolds and of Lie algebroids have been proposed, the latter being usually presented as a generalization of the former. In this note it is shown that the latter method is actually related to (and may be derived from) a particular case of the former if one regards dual of Lie algebroids as special Poisson manifolds. The core of the proof is the fact, discussed in the second part of this note, that coisotropic submanifolds of a (twisted) Poisson manifold are in one-to-one correspondence with possibly singular Lagrangian subgroupoids of source-simply-connected (twisted) symplectic groupoids.

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