Poisson geometry
The course offers an introduction to Poisson geometry. Topics include:
Poisson brackets and bivectors. Examples (linear and log-simpletic Poisson structures, Poisson Lie groups and their homogeneous spaces); Poisson, co-isotropic, and co-symplectic subvarieties; Local structure: Weinstein’s decomposition theorem, transversal structure, linearization; Simple foliation; Poisson cohomology, modular class simplical realizations and dual pairs Lie groupoids and algebroids; simplicial groupoids, integration of Poisson structures; Elements of Dirac geometry, Courant algebroids.
References:
H. Bursztyn, A brief introduction to Poisson geometry, In: Advances in Poisson geometry. Advanced Courses in Mathematics — CRM Barcelona, Birkauser.
M. Crainic, R. Fernandes, I. Marcut: Lectures on Poisson geometry. GMS 217, AMS.
A. Cannas da Silva, A. Weinstein: Geometric models for noncommutative algebras. Berkeley lecture notes, AMS.
J.-P. Dufour, N.T. Zung: Poisson structures and their normal forms. Progress in Math., Birkhauser.
H. Bursztyn, A brief introduction to Poisson geometry, In: Advances in Poisson geometry. Advanced Courses in Mathematics — CRM Barcelona, Birkauser.
M. Crainic, R. Fernandes, I. Marcut: Lectures on Poisson geometry. GMS 217, AMS.
A. Cannas da Silva, A. Weinstein: Geometric models for noncommutative algebras. Berkeley lecture notes, AMS.
J.-P. Dufour, N.T. Zung: Poisson structures and their normal forms. Progress in Math., Birkhauser.