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代数拓扑简明教程(第1卷)

代数拓扑简明教程(第1卷)

作者:乔·彼得·梅

出版社:世界图书出版公司

出版时间:2019-09-01

ISBN:9787519266592

定价:¥42.00

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内容简介
  代数拓扑是现代数学的基本部分,这个领域的知识对研究高级的与几何相关的工作(包括拓扑本身、微分几何、代数几何和李群等)来说是必不可少的。本书是一本代数拓扑的简明教程,书里包含了很多首次在教科书中出现的代数拓扑的前沿研究进展。 \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。
目录

Introduction

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Chapter 1. The fundamental group and some of its applications

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Chapter 2. Categorical language and the van Kampen theorem

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Chapter 3. Covering spaces

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Chapter 4. Graphs

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Chapter 5. Compactly generated spaces

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Chapter 6. Cofibrations

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Chapter 7. Fibrations

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Chapter 8. Based cofiber and fiber sequences

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Chapter 9. Higher homotopy groups

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Chapter 10. CW complexes

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Chapter 11. The homotopy excision and suspension theorems

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Chapter 12. A little homological algebra

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Chapter 13. Axiomatic and cellular homology theory

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Chapter 14. Derivations of properties from the axioms

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Chapter 15. The Hurewicz and uniqueness theorems

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Chapter 16. Singular homology theory

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Chapter 17. Some more homological algebra

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Chapter 18. Axiomatic and cellular cohomology theory

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Chapter 19. Derivations of properties from the axioms

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Chapter 20. The Poincar´e duality theorem

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Chapter 21. The index of manifolds; manifolds with boundary

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Chapter 22. Homology, cohomology, and K(π, n)s

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Chapter 23. Characteristic classes of vector bundles

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Chapter 24. An introduction to K-theory

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Chapter 25. An introduction to cobordism

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