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Full Product Details

Author:   Camille Laurent-Gengoux ,  Anne Pichereau ,  Pol Vanhaecke
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Volume:   347
Dimensions:   Width: 15.50cm , Height: 2.50cm , Length: 23.50cm
Weight:   7.314kg
ISBN:  

9783642432835

ISBN 10:   3642432832
Pages:   464
Publication Date:   20 September 2014
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
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Table of Contents

​Part I Theoretical Background:1.Poisson Structures: Basic Definitions.- 2.Poisson Structures: Basic Constructions.- 3.Multi-Derivations and Kähler Forms.- 4.Poisson (Co)Homology.- 5.Reduction.- Part II Examples:6.Constant Poisson Structures, Regular and Symplectic Manifolds.- 7.Linear Poisson Structures and Lie Algebras.- 8.Higher Degree Poisson Structures.- 9.Poisson Structures in Dimensions Two and Three.- 10.R-Brackets and r-Brackets.- 11.Poisson–Lie Groups.- Part III Applications:12.Liouville Integrable Systems.- 13.Deformation Quantization.- A Multilinear Algebra.- B Real and Complex Differential Geometry.- References.- Index.- List of Notations.  

Reviews

From the reviews: This book is an excellent presentation of Poisson geometry, its applications and related topics. ... This book is suitable for those who have a solid foundation of differential geometry and Lie algebras. The reader will understand why Poisson geometry is such an interesting and important subject. (Zhuo Chen, zbMATH, Vol. 1284, 2014) This book provides a comprehensive introduction to Poisson structures. ... Exercises are given at the end of each chapter ... to help readers understand the basic theory. ... This is a nice introductory book for both entry level graduate students and advanced researchers who are interested in the subject. (Xiang Tang, Mathematical Reviews, August, 2013) The book under review deals with very exciting (and current) material presented from a fascinating vantage point and should be welcomed by any scholar whose work touches upon the matters ... . its thirteen chapters are peppered with sets of exercises and each chapter comes equipped with supplemental notes that go a bit beyond the text, introduce some historical material, and point to other relevant sources. (Michael Berg, MAA Reviews, November, 2012)

Author Information

"C. Laurent-Gengoux research focus lies on Poisson geometry, Lie-groups and integrable systems. He is the author of 14 research articles. Furthermore, he is committed to teaching and set up several mathematics projects with local high schools. In 2002 he earned his doctorate in mathematics with a dissertation on "" Quelques problèmes analytiques et géométriques sur les algèbres et superalgèbres de champs et superchamps de vecteurs”. A. Pichereau earned her doctorate in mathematics with a dissertation on “Poisson (co)homology and isolated singularities in low dimensions, with an application in the theory of deformations” under the supervision of P. Vanheacke in 2006. She has since published four journal articles on Poisson structures and contributed to the Proceedings of ""Algebraic and Geometric Deformation Spaces”. P. Vanheacke’s research focus lies on integrable systems, Abelian varieties, Poisson algebra/geometry and deformation theory. In 1991 he earned his doctorate in mathematics with a dissertation on “Explicit techniques for studying two-dimensional integrable systems” and has published numerous research articles since."

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