Book  Introduction to Symplectic Geometry  JeanLouis Koszul

 JeanLouis Koszul 
(reed) 2019 Springer LINK Video
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Offers a unique and unified overview of symplectic geometry, Highlights the differential properties of symplectic manifolds, Great interest for the emerging field of "Geometric Science of Information”
This introductory book offers a unique and unified overview of symplectic geometry, highlighting the differential properties of symplectic manifolds. It consists of six chapters: Some Algebra Basics, Symplectic Manifolds, Cotangent Bundles, Symplectic Gspaces, Poisson Manifolds, and A Graded Case, concluding with a discussion of the differential properties of graded symplectic manifolds of dimensions (0,n). It is a useful reference resource for students and researchers interested in geometry, group theory, analysis and differential equations. This book is also inspiring in the emerging field of Geometric Science of Information, in particular the chapter on Symplectic Gspaces, where JeanLouis Koszul develops JeanMarie Souriau's tools related to the nonequivariant case of coadjoint action on Souriau’s moment map through Souriau’s Cocycle, opening the door to Lie Group Machine Learning with SouriauFisher metric.
 JeanLouis Koszul 