Introduction to Symplectic Geometry

Jean-Louis Koszul, Yi Ming Zou (Autoren)

Buch | Hardcover

121 Seiten

2019 | 1st ed. 2019
Springer Verlag, Singapore
978-981-13-3986-8 (ISBN)

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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.

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.

Erscheinungsdatum	03.05.2019
Zusatzinfo	9 Illustrations, color; 10 Illustrations, black and white; L, 121 p. 19 illus., 9 illus. in color.
Verlagsort	Singapore
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Themenwelt	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	Cotangent Bundles • G-spaces • Poisson Manifolds • supermanifolds • Symplectic Geometry
ISBN-10	981-13-3986-4 / 9811339864
ISBN-13	978-981-13-3986-8 / 9789811339868
Zustand	Neuware