Description
Book SynopsisTrade ReviewThis excellent book will be very useful for students and researchers wishing to learn the basics of Poisson geometry, as well as for those who know something about the subject but wish to update and deepen their knowledge. The authors' philosophy that Poisson geometry is an amalgam of foliation theory, symplectic geometry, and Lie theory enables them to organize the book in a very coherent way."" —Alan Weinstein, University of California at Berkeley
""This well-written book is an excellent starting point for students and researchers who want to learn about the basics of Poisson geometry. The topics covered are fundamental to the theory and avoid any drift into specialized questions; they are illustrated through a large collection of instructive and interesting exercises. The book is ideal as a graduate textbook on the subject, but also for self-study."" —Eckhard Meinrenken, University of Toronto
Table of Contents
- 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
