Algebraic Topology pdf epub mobi txt 电子书 下载 2025
- 数学
- 代数拓扑
- algebraic_topology
- 拓扑
- 拓扑学
- Mathematics
- 经典
- Topology
- 代数拓扑
- 同调论
- 上同调论
- 基本群
- 覆盖空间
- 流形
- 同伦理论
- 单纯复形
- 纤维丛
- 示性类
具体描述
In most mathematics departments at major universities one of the three or four basic first-year graduate courses is in the subject of algebraic topology. This introductory textbook in algebraic topology is suitable for use in a course or for self-study, featuring broad coverage of the subject and a readable exposition, with many examples and exercises. The four main chapters present the basic material of the subject: fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory generally. The author emphasizes the geometric aspects of the subject, which helps students gain intuition. A unique feature of the book is the inclusion of many optional topics which are not usually part of a first course due to time constraints, and for which elementary expositions are sometimes hard to find. Among these are: Bockstein and transfer homomorphisms, direct and inverse limits, H-spaces and Hopf algebras, the Brown representability theorem, the James reduced product, the Dold-Thom theorem, and a full exposition of Steenrod squares and powers. Researchers will also welcome this aspect of the book.
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用户评价
补标记，17年底读的。作者个人主页有电子版pdf和errata。
评分关于homology的讨论一上来就太具体了，如果先看过axioms再具体的homology会简单很多。但是还是要给5星，因为无hatcher，无代数拓扑。
评分Reread for Professor Maryam Mirzakhani - most attractive woman I've ever known.
评分除了喜欢啰嗦一堆废话以外，还是挺好的
评分太细化了
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