#
nLab

symplectic leaf

### Context

#### Symplectic geometry

# Contents

## Idea

For $(X, \{-,-\})$ a Poisson manifold, a *symplectic leaf* is a maximal submanifold $Y \hookrightarrow X$ on which the Poisson bracket restricts to a symplectic manifold structure.

$X$ is foliated by its symplectic leaves.

## References

Regular foliations by symplectic leafs have originally been found and studied in

- F. Bayen, M. Flato, C. Fronsdal, A. Lichnerovicz & D. Sternheimer,
*Deformation theory and quantization*, Ann. Phys. I l l (1978) 61-151.

A detailed technical review is in the notes

- Jordan Watts,
*An introduction to Poisson manifolds* (2007) (pdf)

Revised on April 23, 2013 20:50:26
by

Urs Schreiber
(131.174.42.75)