Rezensionen / Stimmen
This 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
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ISBN-13
978-1-4704-6667-1 (9781470466671)
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Schweitzer Klassifikation
Marius Crainic, Utrecht University, The Netherlands.
Rui Loja Fernandes, University of Illinois at Urbana-Champaign, IL.
Ioan Marcut, Radboud University, Nijmegen, The Netherlands.
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