nLab Poisson geometry

Idea

Poisson geometry is primarily the study of Poisson manifolds and the foliation by symplectic leaves, but more generally it involves a host of induced and related structures that appear notably in the study of deformation quantization of Poisson manifolds, such as their Poisson Lie algebroids, coisotropic submanifolds, symplectic Lie groupoids etc.

Related concepts

• Poisson manifold

• symplectic geometry

References

Monographs:

• Marius Crainic, Rui Loja Fernandes, Lectures on Poisson Geometry, Graduate Studies in Mathematics 217, Amer. Math. Soc. (2021) [ISBN:978-1-4704-6430-1]

Exposition and survey of the field:

• Ivan Contreras, Diego Martinez, Nicolas Martinez, Diego Rodriguez: Symplectic Geometry, Poisson Geometry, and Beyond [arXiv:2411.12551]

For more see the references at Poisson manifold.