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代數(shù)拓?fù)浜喢鹘坛蹋ǖ?卷)

代數(shù)拓?fù)浜喢鹘坛蹋ǖ?卷)

定 價:¥79.00

作 者: 喬·彼得·梅,凱思琳·龐托
出版社: 世界圖書出版公司
叢編項:
標(biāo) 簽: 暫缺

ISBN: 9787519266424 出版時間: 2019-09-01 包裝:
開本: 頁數(shù): 字?jǐn)?shù):  

內(nèi)容簡介

  《代數(shù)拓?fù)浜喢鹘坛蹋ǖ?卷)》里包含了代數(shù)拓?fù)鋵W(xué)的入門知識,如基本群、覆疊空間、同倫、同調(diào)和上同調(diào)等,這本《代數(shù)拓?fù)浜喢鹘坛?(第2卷)》里則介紹了更多標(biāo)準(zhǔn)代數(shù)拓?fù)浣炭茣ǔ]有提及的重要內(nèi)容,如拓?fù)淇臻g的局部化與完備化、模型范疇、Hopf代數(shù)等。 \n

作者簡介

  喬·彼得·梅(Jon Peter May)是美國著名數(shù)學(xué)家,芝加哥大學(xué)教授,研究領(lǐng)域為代數(shù)拓?fù)渑c范疇論,他是抽象同倫論的先驅(qū)之一,提出了operads以及梅譜序列。凱思琳·龐托(Kathleen Ponto)是美國肯塔基大學(xué)教授。

圖書目錄

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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