Introduction to Symplectic Geometry

1. Auflage 2019
ISBN: 978-981-13-3986-8
Verlag: Springer Nature Singapore

Buch, Englisch, 121 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 430 g

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Zou, Yi Ming

Koszul, Jean-Louis

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

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

Über Autor(innen)

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