代数拓扑简明教程
豆瓣
第1卷
A Concise Course in Algebraic Topology
J. P. May
简介
《代数拓扑简明教程（第1卷）》里包含了代数拓扑学的入门知识，如基本群、覆叠空间、同伦、同调和上同调等，这本《代数拓扑简明教程 （第2卷）》里则介绍了更多标准代数拓扑教科书通常没有提及的重要内容，如拓扑空间的局部化与完备化、模型范畴、Hopf代数等。
目录
Introduction
Chapter 1. The fundamental group and some of its applications
Chapter 2. Categorical language and the van Kampen theorem
Chapter 3. Covering spaces
Chapter 4. Graphs
Chapter 5. Compactly generated spaces
Chapter 6. Cofibrations
Chapter 7. Fibrations
Chapter 8. Based cofiber and fiber sequences
Chapter 9. Higher homotopy groups
Chapter 10. CW complexes
Chapter 11. The homotopy excision and suspension theorems
Chapter 12. A little homological algebra
Chapter 13. Axiomatic and cellular homology theory
Chapter 14. Derivations of properties from the axioms
Chapter 15. The Hurewicz and uniqueness theorems
Chapter 16. Singular homology theory
Chapter 17. Some more homological algebra
Chapter 18. Axiomatic and cellular cohomology theory
Chapter 19. Derivations of properties from the axioms
Chapter 20. The Poincar´e duality theorem
Chapter 21. The index of manifolds; manifolds with boundary
Chapter 22. Homology, cohomology, and K(π, n)s
Chapter 23. Characteristic classes of vector bundles
Chapter 24. An introduction to K-theory
Chapter 25. An introduction to cobordism
