Introduction to Symplectic Geometry

ISBN-13: 9789811339868 / Angielski / Twarda / 2019 / 121 str.

Jean-Louis Koszul; Yiming Zou

Recenzje

"This book is of great interest for the emerging field of Geometric Science of Information, in which the generalization of the Fisher metric is at the heart of the extension of classical tools from Machine Learning and Artificial Intelligence to deal with more abstract objects living in homogeneous manifolds, groups, and structured matrices.'" (Pablo Suárez-Serrato, zbMATH 1433.53002, 2020)

Spis treści

Some Algebra Basics.- Symplectic Manifolds.- Cotangent Bundles.- Symplectic G-spaces.- Poisson Manifolds.- A Graded Case.

O autorze

Jean Louis Koszul, born in 1921, was a French Mathematician. He was a member of 2^nd generation of Bourbaki, also a member of French Academy of Sciences.  Jean-Louis Koszul passed away on January 12^th 2018, at the age of 97.

Blurb

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.