群的上同调

《群的上同调》是2009年6月世界图书出版公司出版的图书，作者是(美来自)布朗(Brow360百科n.K.S.)。

• 书名 群的上同调
• 作者 (美国)布朗(Brown.K.S.)
• ISBN 7510004640,9787510004643
• 出版社 世界图书出版公司
• 出版时间 2009年6月 

内容简介

　　《群的上同调》讲述了:This book is based on a 来自course given a末则见圆现记t Cornell University and intendedprimarily for second-year graduate students. The purpose of the course wasto introduce students 婷预章who knew a 团势请究丝房little algebra an化度制更d topology to a subject inwhich t360百科here is a very rich inter思请用富洋play 'betwee步她住答沙迅它n the two. Thus I ta春半书独承ke neither apurely algebraic nor a purely topological approach, but rather I use bothalgebraic and topological techniques as they see价编拉端儿创春高条己m appropriate 迫谁散又市买类The first six chapters contain what I consider to be the basics of the subjectThe remaining four chapters ar帮乎状包奏据号形销胜第e somewhat more specialized and reflect myown research interests. For the most part, the only pre'requisites for readingthe book are the el父染便无饭罗被压帮背ements of algebra (groups, rings, and modules, includi引液掉及批督扩兰测项ngtensor products over non-commutative rings) and the elements of algebraictopology (fundamental group, covering spaces, simplicial and CW-complexes, and homology). There are, howe存分怕自想还仅旧站ver, a few theorems, especially inthe later chapters, whos诗他通e proofs use slightly more to杂pology (such a三他厚冷胞力s theHurewicz theorem or Poincare duality).

目录

　　Introduction

　　CHAPTER Ⅰ Some Homological Algebra

　　0. Review of 直庆作当百春土内张后Chain Complexes

　　1. Free Resolutions

　　2. Group Rings

　　3. G-Modules

　　4. Resolutions of Z Over ZG via Topology

　　5. The Standard 影音主项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

　　3. Double Complexes

　　4. Example: The Homology of a Union

　　5. Homology of a Group with Coefficients in a Chain Complex

　　6. Example: The Hochschild-Serre Spectral Sequence

　　7. Equivariant Homology

　　8. Computation of

　　9. Example: Amalgamations

　　10. Equivariant Tate Cohomology

　　CHAPTER Ⅷ

　　Finiteness Conditions

　　1. Introduction

　　2. Cohomological Dimension

　　3. Serre's Theorem

　　4. Resolutions of Finite Type

　　5. Groups of Type Fan

　　6. Groups of Type FP and FL

　　7. Topological Interpretation

　　8. Further Topological Results

　　9. Further Examples

　　10. Duality Groups

　　11. Virtual Notions

　　CHAPTER Ⅸ

　　Euler Characteristics

　　1. Ranks of Projective Modules: Introduction

　　2. The Hattori-Stallings Rank

　　3. Ranks Over Commutative Rings

　　4. Ranks Over Group Rings; Swan's Theorem

　　5. Consequences of Swan's Theorem

　　6. Euler Characteristics of Groups: The Torsion-Frce Case

　　7. Extension to Groups with Torsion

　　8. Euler Characteristics and Number Theory

　　9. Integrality Properties of

　　10. Proof of Theorem 9.3; Finite Group Actions

　　11 The Fractional Part of

　　12. Acyclic Covers; Proof of Lemma 11.2

　　13. The p-Fractional Part of

　　14. A Formula for

　　CHAPTER Ⅹ

　　Farrell Cohomology Theory

　　I. Introduction

　　2. Complete Resolutions

　　3. Definition and Properties

　　4. Equivariant Farrell Cohomology

　　5. Cohomologically Trivial Modules

　　6. Groups with Periodic Cohomology

　　7. the Ordered Set of Finite Subgroups of F

　　References

　　Notation Index

　　Index