代数拓扑简明教程(第2卷) 本书特色

《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。

代数拓扑简明教程(第2卷) 内容简介

《代数拓扑简明教程（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。

代数拓扑简明教程(第2卷) 目录

Introduction PART 1. Preliminaries: Basic Homotopy Theory and Nilpotent Spaces Chapter 1. Cofibrations and fibrations Chapter 2. Homotopy colimits and homotopy limits; lim^1 Chapter 3. Nilpotent spaces and Postnikov towers Chapter 4. Detecting nilpotent groups and spaces PART 2. Localizations of Spaces at Sets of Primes Chapter 5. Localizations of nilpotent groups and spaces Chapter 6. Characterizations and properties of localizations Chapter 7. Fracture theorems for localization: groups Chapter 8. Fracture theorems for localization: spaces Chapter 9. Rational H-spaces and fracture theorems PART 3. Completions of Spaces at Sets of Primes Chapter 10. Completions of nilpotent groups and spaces Chapter 11. Characterizations and properties of completions Chapter 12. Fracture theorems for completion: groups Chapter 13. Fracture theorems for completion: spaces PART 4. An Introduction to Model Category Theory Chapter 14. An introduction to model category theory Chapter 15. Cofibrantly generated and proper model categories Chapter 16. Categorical perspectives on model categories Chapter 17. Model structures on the category of spaces Chapter 18. Model structures on categories of chain complexes Chapter 19. Resolution and localization model structures PART 5. Bialgebras and Hopf Algebras Chapter 20. Bialgebras and Hopf algebras Chapter 21. Connected and component Hopf algebras Chapter 22. Lie algebras and Hopf algebras in characteristic zero Chapter 23. Restricted Lie algebras and Hopf algebras in characteristic p Chapter 24. A primer on spectral sequences

代数拓扑简明教程(第2卷) 作者简介

乔·彼得·梅（Jon Peter May）是美国著名数学家，芝加哥大学教授，研究领域为代数拓扑与范畴论，他是抽象同伦论的先驱之一，提出了operads以及梅谱序列。凯思琳·庞托（Kathleen Ponto）是美国肯塔基大学教授。

自然科学 数学 代数数论组合理论

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