Letters in Mathematical Physics

, Volume 67, Issue 1, pp 33–48 | Cite as

On the Integration of Poisson Manifolds, Lie Algebroids, and Coisotropic Submanifolds

  • Alberto S. Cattaneo>


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 Letter 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 Letter, 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.

coisotropic submanifold Lagrangian subgroupoid Lie algebroid Poisson manifold symplectic groupoid symplectic reduction twisted Poisson manifold 


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© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Alberto S. Cattaneo>
    • 1
  1. 1.Institut für MathematikUniversität Zürich-IrchelZürichSwitzerland

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