Izu Vaisman (auth.)9780817650162, 9783764350161, 0817650164, 3764350164
“The book serves well as an introduction and an overview of the subject and a long list of references helps with further study.”
— Zbl. Math.
“The book is well done…should be an essential purchase for mathematics libraries and is likely to be a standard reference for years to come, providing an introduction to an attractive area of further research.” — Mathematical Reviews
“The importance and actuality of the subject, as well as the very rigorous and didactic presentation of the content, make out of this book a valuable contribution to current mathematics. The book is intended first of all to mathematicians, but it can be interesting also for a wide circle of readers, including mechanicists and physicists.” — Mathematica
Table of contents :
Front Matter….Pages i-vii
Introduction….Pages 1-3
The Poisson Bivector and the Schouten-Nijenhuis Bracket….Pages 5-17
The Symplectic Foliation of a Poisson Manifold….Pages 19-30
Examples of Poisson Manifolds….Pages 31-40
Poisson Calculus….Pages 41-62
Poisson Cohomology….Pages 63-82
An Introduction to Quantization….Pages 83-96
Poisson Morphisms, Coinduced Structures, Reduction….Pages 97-114
Symplectic Realizations of Poisson Manifolds….Pages 115-133
Realizations of Poisson Manifolds by Symplectic Groupoids….Pages 135-159
Poisson-Lie Groups….Pages 161-188
Back Matter….Pages 189-207
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