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© 2019

Introduction to Symplectic Geometry

  • 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

Textbook

Table of contents

  1. Front Matter
    Pages i-l
  2. Jean-Louis Koszul, Yi Ming Zou
    Pages 1-19
  3. Jean-Louis Koszul, Yi Ming Zou
    Pages 21-55
  4. Jean-Louis Koszul, Yi Ming Zou
    Pages 57-73
  5. Jean-Louis Koszul, Yi Ming Zou
    Pages 75-90
  6. Jean-Louis Koszul, Yi Ming Zou
    Pages 91-107
  7. Jean-Louis Koszul, Yi Ming Zou
    Pages 109-116
  8. Back Matter
    Pages 117-121

About this book

Introduction

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.

Keywords

Symplectic Geometry Cotangent Bundles G-spaces Poisson Manifolds supermanifolds

Authors and affiliations

  1. 1.Institut FourierUniversité Grenoble AlpesGières, GrenobleFrance
  2. 2.Department of Mathematical SciencesUniversity of Wisconsin-MilwaukeeMilwaukeeUSA

About the authors

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.

Bibliographic information

Industry Sectors
Aerospace

Reviews

“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)