Lectures on Poisson Geometry

ISBN-13: 9781470466671

Marius Crainic;Rui Loja Fernandes;Ioan Marcut

Spis treści

• Basic concepts: Poisson brackets
• Poisson bivectors
• Local structure of Poisson manifolds
• Notes and references for Part 1
• Poisson geometry around leaves: Symplectic leaves and the symplectic foliation
• Poisson transversals
• Symplectic realizations
• Dirac geometry
• Submanifolds in Poisson geometry
• Notes and references for Part 2
• Global aspects: Poisson cohomology
• Poisson homotopy
• Contravariant geometry and connections
• Notes and references for Part 3
• Symplectic groupoids: Complete symplectic realizations
• A crash course on Lie groupoids
• Symplectic groupoids
• Notes and references for Part 4
• Appendices: Lie groups
• Symplectic structures
• Foliations
• Groupoids: Conventions and choices
• Bibliography
• Index