作者：（法）帕特里克·伊格莱西亚斯-泽穆尔（PatrickIglesias-Zemmour） 著
出版社：世界图书出版公司
出版日期：2025
ISBN：9787523218419
电子书格式：pdf/epub/txt
网盘下载地址：下载广义微分几何讲义
内容简介
《广义微分几何讲义》是已出版的《广义微分几何》（广义微分几何领域第一本教材）的配套教学笔记，一半源自作者在汕头大学的授课经历，一半则是作者在同各方学者多年研究探讨后的研究成果、思考、练习等作者希望与读者分享的笔记。全书以时间线为轴，讲述广义微分几何领域的起源和发展，编排合理，每章篇头都有总述、定义、理论等讲解，辅以推论过程，由简到难，自然过渡到结论，很符合授课讲义的风格，其后还有习题、问题、思考探讨等用以巩固讲义知识，并启发思考，对研究微分几何或数学物理的学生与研究人员极为有用。
作者简介
帕特里克·伊格莱西亚斯-泽穆尔（Patrick Iglesias-Zemmour）是法国国家科学研究中心研究员，也是以色列希伯来大学的长期客座教授。他以辛几何和广义微分几何的研究而闻名。他所著的《广义微分几何》（Diffeology）是该领域国际上的shou部教材。《广义微分几何讲义》是作者多年研究成果的全新呈现，与《广义微分几何》相互呼应。
相关资料
These lecture notes are aimed at students interested in differential geometry, especially in directions not ordinarily covered by the classical theory.They are divided into two parts: firstly, a series of lectures, which were presented as part of a special program at Shantou University. They summarize the major chapters of diffeology: axiomatics, categories, homotopy, Cartan calculus, fiber bundles, etc. They serve as an introduction to the various sections of diffeology in the corresponding chapters of the Diffeology textbook, which remains the formal basis for a course in diffeology. They do not replace the textbook, but serve as a kind of springboard.
本书特色
本书是国际上Diffeology研究领军人物Patrick Iglesias-Zemmour所撰写的讲义，是已出版的Diffeology领域名著《广义微分几何》的配套教学笔记。
目录
Preface
At the Beginning
Diffeology, the Axiomatic
The Irrational Tori 8
Generating Families, Dimension
Cartan-De-Rham Calculus
Diffeology Fiber Bundles
Homotopy Theory in Diffeology
Local Diffeology, Modeling
Modeling: Manifolds, Orbifolds and Quasifolds
Symplectic Mechanics and Diffeology
Diffeology and Non-Commutative Geometry
Functional Diffeology on Fourier Coefffcients
Smooth Function on Periodic Functions
Symplectic Diffeology on Smooth Periodic Functions
Infinite Torus Action on Smooth Periodic Functions
Basic 1-Forms on Principal Fiber Bundles
Differential of Holonomy for Torus Bundles
Non-symplectic manifold with injective univ. moment map
On Riemannian Metric in Diffeology
A Few Half-Lines
1-Forms on Half-Lines
1-Forms on the Subset Half-Line
Cotangent Space of the Half-Line
1-Forms on Half-Spaces
p-Forms on Half-Spaces
p-Forms on Corners
Differential Forms on the Cross
A note on Hamiltonian Diffeomorphisms
Differential of a Lie-Group Valued Function
The Geodesics of the 2-Torus
The Use of the Moment Map in Geodesic Calculus
The Parasymplectic Space of Geodesics Trajectories
Diffeomorphisms of Geod(T2)
The Diffeomorphisms of the Square
Diffeological Spaces are Locally Connected
Vague Adjunction of a Point to a Space
Embedding a Diffeological Space Into its Powerset
Foliations and Diffeology
Klein Stratiffcation of Diffeological Spaces
Lagrange’s Equations of Motion
Poisson Bracket in Diffeology
Smooth embeddings and smoothly embedded subsets
Seifert Orbifolds
Symplectic spaces without Hamiltonian diffeomorphisms
The Diffeology Framework of General Covariance
Postface: The Beginning of Diffeological Spaces
Appendix: A Categorical Approach to Diffeology
Bibliography
