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作者: 布朗

出版社: 世界图书出版公司

出版时间: 2009-06

版次: 1

ISBN: 9787510004643

定价: 38.00

装帧: 平装

开本: 24开

纸张: 胶版纸

页数: 306页

原版书名: Cohomology of Groups

分类: 教材教辅考试>教材>大学教材>工程技术

18人买过

. Introduction

CHAPTER Ⅰ Some Homological Algebra

　0. Review of Chain Complexes

　1. Free Resolutions

　2. Group Rings

　3. G-Modules

　4. Resolutions of Z Over ZG via Topology

　5. The Standard Resolution

　6. Periodic Resolutions via Free Actions on Spheres

　7. Uniqueness of Resolutions

　8. Projective Modules

　Appendix.  Review of Regular Coverings

CHAPTER Ⅱ The Homology of a Group

　1. Generalities

　2. Co-invariants

　3. The Definition of H,G

　4. Topological Interpretation

　5. Hopf's Theorems

　6. Functoriality

　7. The Homology of Amalgamated Free Products

　Appendix. Trees and Amalgamations

CHAPTER Ⅲ Homology and Cohomology with Coefficients

　0. Preliminaries on X G and HomG

　1. Definition of H,(G, M) and H*(G, M)

　2. Tor and Ext

  3. Extension and Co-extension of Scalars

  4. Injective Modules

  5. Induced and Co-induced Modules

  6. H, and H* as Functors of the Coefficient Module

  7. Dimension Shifting

  8. H, and H* as Functors of Two Variables

  9. The Transfer Map

　10. Applications of the Transfer

CHAPTER Ⅳ Low Dimensional Cohomology and Group Extensions

　1. Introduction

　2. Split Extensions

　3. The Classification of Extensions with Abelian Kernel

　4. Application: p-Groups with a Cyclic Subgroup of Index p

　5. Crossed Modules and H3 (Sketch)

　6. Extensions With Non-Abelian Kernel (Sketch)

CHAPTER Ⅴ Products

　1. The Tensor Product of Resolutions

　2. Cross-products

　3. Cup and Cap Products

　4. Composition Products

　5. The Pontryagin Product

　6. Application :  Calculation of the Homology of an Abelian Group

CHAPTER Ⅵ Cohomology Theory of Finite Groups

　1. Introduction

　2. Relative Homological Algebra

　3. Complete Resolutions

　4. Definition of H*

　5. Properties of H*

　6. Composition Products

　7. A Duality Theorem

　8. Cohomologically Trivial Modules

　9. Groups with Periodic Cohomology

CHAPTER Ⅶ Equivariant Homology and Spectral Sequences

　1. Introduction

　2. The Spectral Sequence of a Filtered Complex

　……

CHAPTER Ⅷ Finiteness Conditions

CHAPTER Ⅸ Euler Characteristics

CHAPTER Ⅹ Farrell Cohomology Theory

References

Notation Index

Index
内容简介:
.
目录:
Introduction

CHAPTER Ⅰ Some Homological Algebra

　0. Review of Chain Complexes

　1. Free Resolutions

　2. Group Rings

　3. G-Modules

　4. Resolutions of Z Over ZG via Topology

　5. The Standard Resolution

　6. Periodic Resolutions via Free Actions on Spheres

　7. Uniqueness of Resolutions

　8. Projective Modules

　Appendix.  Review of Regular Coverings

CHAPTER Ⅱ The Homology of a Group

　1. Generalities

　2. Co-invariants

　3. The Definition of H,G

　4. Topological Interpretation

　5. Hopf's Theorems

　6. Functoriality

　7. The Homology of Amalgamated Free Products

　Appendix. Trees and Amalgamations

CHAPTER Ⅲ Homology and Cohomology with Coefficients

　0. Preliminaries on X G and HomG

　1. Definition of H,(G, M) and H*(G, M)

　2. Tor and Ext

  3. Extension and Co-extension of Scalars

  4. Injective Modules

  5. Induced and Co-induced Modules

  6. H, and H* as Functors of the Coefficient Module

  7. Dimension Shifting

  8. H, and H* as Functors of Two Variables

  9. The Transfer Map

　10. Applications of the Transfer

CHAPTER Ⅳ Low Dimensional Cohomology and Group Extensions

　1. Introduction

　2. Split Extensions

　3. The Classification of Extensions with Abelian Kernel

　4. Application: p-Groups with a Cyclic Subgroup of Index p

　5. Crossed Modules and H3 (Sketch)

　6. Extensions With Non-Abelian Kernel (Sketch)

CHAPTER Ⅴ Products

　1. The Tensor Product of Resolutions

　2. Cross-products

　3. Cup and Cap Products

　4. Composition Products

　5. The Pontryagin Product

　6. Application :  Calculation of the Homology of an Abelian Group

CHAPTER Ⅵ Cohomology Theory of Finite Groups

　1. Introduction

　2. Relative Homological Algebra

　3. Complete Resolutions

　4. Definition of H*

　5. Properties of H*

　6. Composition Products

　7. A Duality Theorem

　8. Cohomologically Trivial Modules

　9. Groups with Periodic Cohomology

CHAPTER Ⅶ Equivariant Homology and Spectral Sequences

　1. Introduction

　2. The Spectral Sequence of a Filtered Complex

　……

CHAPTER Ⅷ Finiteness Conditions

CHAPTER Ⅸ Euler Characteristics

CHAPTER Ⅹ Farrell Cohomology Theory

References

Notation Index

Index

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