Poisson Structures (eBook)

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.

​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.