可微流形和李群基础
2004-4
世界图书出版公司
Frank W.Warner
272
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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.
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
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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。