微分拓扑学

出版时间：2000-12  出版社：北京世图  作者：Morris W.Hirsch  页数：224  
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内容概要

This book presents some of the basic topological ideas used in studying differentiable manifolds and maps. Mathematical prerequisites have been kept to a minimum; the standard course in analysis and general topology is adequate preparation. An appendix briefly summarizes some of the background material. In order to emphasize the geometrical and intuitive aspects of differential topology, I have avoided the use of algebraic topology, except in a few isolated places that can easily be skipped. For the same reason I make no use of differential forms or tensors.

书籍目录

IntrodttctionChapter 1: Manifolds and Maps  0. Submanifolds of Rn k  1. Differential Structures  2. Differentiable Maps and the Tangent Bundle  3. Embeddings and Immersions  4. Manifolds with Boundary  5. A ConventionChapter 2: Function Spaces  1. The Weak and Strong Topologies on Cr M,N  2. Approximations  3. Approximations on -Manifolds and Manifold Pairs  4. Jets and the Baire Property  5. Analytic ApproximationsChapter 3: Transversality  1. The Morse-Sard Theorem  2. TransversalityChapter 4: Vector Bundles and Tubular Neighborhoods  1. Vector Bundles  2. Constructions with Vector Bundles  3. The Classification of Vector Bundles  4. Oriented Vector Bundles  5. Tubular Neighborhoods  6. Collars and Tubular Neighborhoods of Neat Submanifolds  7. Analytic Differential StructuresChapter 5: Degrees, Intersection Numbers, and the Euler Characteristic  1. Degrees of Maps  2. Intersection Numbers and the Euler Characteristic  3. Historical RemarksChapter 6: Morse Theory  1. Morse Functions  2. Differential Equations and Regular Level Surfaces  3. Passing Critical Levels and Attaching Cells  4. CW-ComplexesChapter 7: Cobordism  1. Cobordism and Transversality  2. The Thom HomomorphismChapter 8: Isotopy  1. Extending Isotopies  2. Gluing Manifolds Together  3. Isotopies of DisksChapter 9: Surfaces  1. Models of Surfaces  2. Characterization of the Disk  3. The Classification of Compact SurfacesBibliographyAppendixIndex

用户评论 (总计13条)

•   虽然微分拓扑现在有些落伍了，但是学习一下古典微分拓扑还是对自身数学素养非常有帮助的！建议这本书学习！
•   看了一点，很不错
•   内容本身有一定难度的，需要认真理解
•   此书很适合初学者，很易读，包装也很好，印刷也很好，排版也很好。
  这本微分拓扑内容非常好，我向大家推介这本书。
•   现在收藏着，准备以后看完流形和拓扑看
•   微分拓扑经典教材，张筑生书的序言里提到过。
•   本书为GTM系列的vol 33。内容简明，特色之处是有Cobordism（配边论）。玩微分拓扑的兄弟手上有一本GTM33貌似是必须的。
  另外在这里希望当当能进全套GTM。让国内科技人士能靠看书的来提升自己的数学素养
•   怎么说呢？起点其实很高，需要读者积累一定对流形的认识之后再看很合适。前奏的话可以看看pollack的书，很好的一本书，很直观。
•   书还没有仔细看，整体上感觉是很好的教材。GTM系列的丛书多可作为学习数学的经典教材。
•   书挺喜欢，质量不错 发票 都很满意
•   这本书别看只有200多页，但是难度不小。特别是有些习题很难。
•   书本质量很好，内容当然更不用说。
•   Hirsch的微分拓扑学确实是一本难得的好书！非常超值！