辛几何引论(英文版)

内容简介

[

辛几何是近几十年发展起来的新的重要数学分支。本书是辛几何（新流形）的入门性读物。。全书分为六章，分别是代数基础、新流形、余切丛、辛G-空间、Poisson流形、一个分级情形。前三章是重要的基本概念，后三章论述有关的应用。

]

目录

Contents1 Some Algebra Basics 11.1 Skew-Symmetric Forms 11.2 0rthogonality Defined by a Skew-Symmetric 2-Form 31.3 Symplectic Vector Spaces， Symplectic Bases 61.4 The Canonical Linear Representation of s/(2， k) in the Algebra of the Skew-Symmetric Forms on a Symplectic Vector Space 81.5 Symplectic Groups 111.6 Symplectic Complex Structures 162 Symplectic Manifolds 212.1 Symplectic Structures on Manifolds 212.2 0perators of the Algebra of Differential Forms on a Symplectic2.3 Symplectic Coordinates 302.4 Hamiltonian Vector Fields and Symplectic Vector Fields 352.5 Poisson Brackets Under Symplectic Coordinates 442.6 Submanifolds of Symplectic Manifolds 483 Cotangent Bundles 573.1 Liouville Forms and Canonical Symplectic Structures on Cotangent Bundles 573.2 Symplectic Vector Fields on a Cotangent Bundle 613.3 Lagrangian Submanifolds of a Cotangent Bundle 684 Symplectic G-Spaces 754.1 Definitions and Examples 764.2 Hamiltonian q-Spaces and Moment Maps 794.3 Equivariance of Moment Maps 875 Poisson Marufolds 915.1 The Structure of a Poisson Manifold 915.1.1 The Schouten-Nijenhuis Bracket 915.2 The Leaves of a Poisson Manifold 955.3 Poisson Structures on the Dual of a Lie Algebra 986 A Graded Case 1096.1 (0， n)-Dimensional Supermanifolds 1096.2 (0， n)-Dimensional Symplectic Supermanifolds 1146.3 The Canonical Symplectic Structure on TP 115Bibliography 117

封面

书名:辛几何引论(英文版)

作者:（法）J.柯歇尔，邹异明

页数:176

定价:¥88.0

出版社:科学出版社

出版日期:2018-06-01

ISBN:9787030613479

PDF电子书大小:64MB 高清扫描完整版