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代数拓扑简明教程(第2卷)

代数拓扑简明教程(第2卷)

定 价:¥79.00

作 者: 乔·彼得·梅,凯思琳·庞托
出版社: 世界图书出版公司
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ISBN: 9787519266424 出版时间: 2019-09-01 包装:
开本: 页数: 字数:  

内容简介

  《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。 \n

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。

图书目录

Introduction

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PART 1. Preliminaries: Basic Homotopy Theory and Nilpotent Spaces

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Chapter 1. Cofibrations and fibrations

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Chapter 2. Homotopy colimits and homotopy limits; lim^1

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Chapter 3. Nilpotent spaces and Postnikov towers

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Chapter 4. Detecting nilpotent groups and spaces

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PART 2. Localizations of Spaces at Sets of Primes

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Chapter 5. Localizations of nilpotent groups and spaces

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Chapter 6. Characterizations and properties of localizations

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Chapter 7. Fracture theorems for localization: groups

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Chapter 8. Fracture theorems for localization: spaces

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Chapter 9. Rational H-spaces and fracture theorems

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PART 3. Completions of Spaces at Sets of Primes

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Chapter 10. Completions of nilpotent groups and spaces

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Chapter 11. Characterizations and properties of completions

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Chapter 12. Fracture theorems for completion: groups

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Chapter 13. Fracture theorems for completion: spaces

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PART 4. An Introduction to Model Category Theory

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Chapter 14. An introduction to model category theory

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Chapter 15. Cofibrantly generated and proper model categories

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Chapter 16. Categorical perspectives on model categories

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Chapter 17. Model structures on the category of spaces

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Chapter 18. Model structures on categories of chain complexes

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Chapter 19. Resolution and localization model structures

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PART 5. Bialgebras and Hopf Algebras

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Chapter 20. Bialgebras and Hopf algebras

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Chapter 21. Connected and component Hopf algebras

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Chapter 22. Lie algebras and Hopf algebras in characteristic zero

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Chapter 23. Restricted Lie algebras and Hopf algebras in characteristic p

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Chapter 24. A primer on spectral sequences

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