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 G-spaces, 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 G-spaces, where Jean-Louis Koszul develops Jean-Marie Souriau's tools related to the non-equivariant case of co-adjoint action on Souriau's moment map through Souriau's Cocycle, opening the door to Lie Group Machine Learning with Souriau-Fisher metric.
Produkt-Info
Auflage
Sprache
Verlagsort
Zielgruppe
Illustrationen
10 s/w Abbildungen, 9 farbige Abbildungen
Bibliographie
Maße
Höhe: 241 mm
Breite: 160 mm
Dicke: 16 mm
Gewicht
ISBN-13
978-981-13-3986-8 (9789811339868)
DOI
10.1007/978-981-13-3987-5
Schweitzer Klassifikation
Jean Louis Koszul, born in 1921, was a French Mathematician. He was a member of 2nd generation of Bourbaki, also a member of French Academy of Sciences. Jean-Louis Koszul passed away on January 12th 2018, at the age of 97.
Some Algebra Basics.- Symplectic Manifolds.- Cotangent Bundles.- Symplectic G-spaces.- Poisson Manifolds.- A Graded Case.