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群的上同调PDF|Epub|txt|kindle电子书版本网盘下载
- （美）布朗编著 著
- 出版社： 世界图书广东出版公司
- ISBN：9787510004643
- 出版时间：2009
- 标注页数：308页
- 文件大小：11MB
- 文件页数：319页
- 主题词：群论－研究生－教材－英文
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图书目录
Introduction1
CHAPTER Ⅰ Some Homological Algebra4
0．Review of Chain Complexes4
1．Free Resolutions10
2．Group Rings12
3．G-Modules13
4．Resolutions of Z Over ZG via Topology14
5．The Standard Resolution18
6．Periodic Resolutions via Free Actions on Spheres20
7．Uniqueness of Resolutions21
8．Projective Modules26
Appendix. Review of Regular Coverings31
CHAPTER Ⅱ The Homology of a Group33
1．Generalities33
2．Co-invariants34
3．The Definition of H*G35
4．Topological Interpretation36
5．Hopf's Theorems41
6．Functoriality48
7．The Homology of Amalgamated Free Products49
Appendix. Trees and Amalgamations52
CHAPTER Ⅲ Homology and Cohomology with Coefficients55
0．Preliminaries on ？G and HomG55
1．Definition of H*(G,M)and H*(G,M)56
2．Tor and Ext60
3．Extension and Co-extension of Scalars62
4．Injective Modules65
5．Induced and Co-induced Modules67
6．H* and H* as Functors of the Coefficient Module71
7．Dimension Shifting74
8．H* and H* as Functors of Two Variables78
9．The Transfer Map80
10．Applications of the Transfer83
CHAPTER Ⅳ Low Dimensional Cohomology and Group Extensions86
1．Introduction86
2．Split Extensions87
3．The Classification of Extensions with Abelian Kernel91
4．Application:p-Groups with a Cyclic Subgroup of Index p97
5．Crossed Modules and H3(Sketch)102
6．Extensions With Non-Abelian Kernel(Sketch)104
CHAPTER Ⅴ Products107
1．The Tensor Product of Resolutions107
2．Cross-products108
3．Cup and Cap Products109
4．Composition Products114
5．The Pontryagin Product117
6．Application:Calculation of the Homology of an Abelian Group121
CHAPTER Ⅵ Cohomology Theory of Finite Groups128
1．Introduction128
2．Relative Homological Algebra129
3．Complete Resolutions131
4．Definition of ？134
5．Properties of ？136
6．Composition Products142
7．A Duality Theorem144
8．Cohomologically Trivial Modules148
9．Groups with Periodic Cohomology153
CHAPTER Ⅶ Equivariant Homology and Spectral Sequences161
1．Introduction161
2．The Spectral Sequence of a Filtered Complex161
3．Double Complexes164
4．Example:The Homology of a Union166
5．Homology of a Group with Coefficients in a Chain Complex168
6．Example:The Hochschild-Serre Spectral Sequence171
7．Equivariant Homology172
8．Computation of d1175
9．Example:Amalgamations178
10．Equivariant Tate Cohomology180
CHAPTER Ⅷ Finiteness Conditions183
1．Introduction183
2．Cohomological Dimension184
3．Serre's Theorem190
4．Resolutions of Finite Type191
5．Groups of Type FPn197
6．Groups of Type FP and FL199
7．Topological Interpretation205
8．Further Topological Results210
9．Further Examples213
10．Duality Groups219
11．Virtual Notions225
CHAPTER Ⅸ Euler Characteristics230
1．Ranks of Projective Modules:Introduction230
2．The Hattori-Stallings Rank231
3．Ranks Over Commutative Rings235
4．Ranks Over Group Rings;Swan's Theorem239
5．Consequences of Swan's Theorem242
6．Euler Characteristics of Groups:The Torsion-Free Case246
7．Extension to Groups with Torsion249
8．Euler Characteristics and Number Theory253
9．Integrality Properties of x(Γ)257
10．Proof of Theorem 9.3;Finite Group Actions258
11．The Fractional Part of x(Γ)261
12．Acyclic Covers;Proof of Lemma 11.2265
13．The p-Fractional Part of x(Γ)266
14．A Formula for xг(？)270
CHAPTER Ⅹ Farrell Cohomology Theory273
1．Introduction273
2．Complete Resolutions273
3．Definition and Properties of ？*(Γ)277
4．Equivariant Farrell Cohomology281
5．Cohomologically Trivial Modules287
6．Groups with Periodic Cohomology288
7．？*(Γ)and the Ordered Set of Finite Subgroups of Γ291
References295
Notation Index301
Index303