可微流形和李群基础

出版时间：2004-4  出版社：世界图书出版公司  作者：Frank W.Warner  页数：272  
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内容概要

This book provides the necessary foundation for students interested in any of the diverse areas of mathematics which require the notion of a differentiable manifold. It is designed as a beginning graduate-level textbook and presumes a good undergraduate training in algebra and analysis plus some knowledge of point set topology, covering spaces, and the fundamental group. It is also intended for use as a reference book since it includes a number of items which are difficult to ferret out of the literature, in particular, thecompleteand self-contained proofs of the fundamental theorems of Hodge and de Rham.

书籍目录

1 MANIFOLDS 　Preliminaries 　Differentiable Manifolds 　The Second Axiom of Countability 　Tangent Vectors and Differentials 　Submanifolds， Diffeomorphisms， and the Inverse Function Theorem 　Implicit Function Theorems 　Vector Fields 　Distributions and the Frobenius Theorem 　Exercises 2 TENSORS AND DIFFERENTIAL FORMS 　Tensor and Exterior Algebras 　Tensor Fields and Differential Forms 　The Lie Derivative 　Differential Ideals 　Exercises 3 IE GROUPS 　Lie Groups and Their Lie Algebras 　Homomorphisms 　Lie Subgroups 　Coverings　Simply Connected Lie Groups　Exponential Map　Continuous Homomorphisms　Closed Subgroups　The Adjoint Representation　Automorphisms and Derivations of Bilinear Operations and Forms　Homgeneous Manifolds　Exercises4 INTEGRATION ON MANIFOLDS5 SHEAVES,COHOMOLGY,AND THE DE RHAM THEOREM6 THE HODGE THEOREMBIBLIOGRAPHYSUPPLEMENT TO BIBLIOGRAPHYINDEX OF NOTATIONINDEX

用户评论 (总计9条)

•   适合在对微分流形或微分拓扑有一个基本的了解后阅读
•   同学推荐的，不错
•   没想到， 书也就是三四包红塔山的价钱
•   经典教材，但不适合初学者。。。要砍掉同调论那一块。。。
•   收到的很快。纯英文教材，备考资料，看着很吃力。
•   经典的著作，推荐读一下
•   虽然早就料到影印版的书质量一般，但是比预期的质量还要差一些。比较失望
•   This is a classical introductory book to differentiable manifold and Lie groups. Usually it is used as the text book for the first year graduate students of math major. Most important ideas of manifold and Lie group (as a mainfold) are listed. Some further topics, such as the Hodge theorem, are also introduced.
•   该领域的名著，篇幅不大，但是却涵盖了大量内容。