Cohomology of groups

Contents......Page all_19785_to_00314.cpc0005.djvu
Introduction......Page all_19785_to_00314.cpc0009.djvu
0. Review of Chain Complexes......Page all_19785_to_00314.cpc0012.djvu
1. Free Resolutions......Page all_19785_to_00314.cpc0018.djvu
2. Group Rings......Page all_19785_to_00314.cpc0020.djvu
3. G-Modules......Page all_19785_to_00314.cpc0021.djvu
4. Resolutions of Z Over ZG via Topology......Page all_19785_to_00314.cpc0022.djvu
5. The Standard Resolution......Page all_19785_to_00314.cpc0026.djvu
6. Periodic Resolutions via Free Actions on Spheres......Page all_19785_to_00314.cpc0028.djvu
7. Uniqueness of Resolutions......Page all_19785_to_00314.cpc0029.djvu
8. Projective Modules......Page all_19785_to_00314.cpc0034.djvu
Appendix. Review of Regular Coverings......Page all_19785_to_00314.cpc0039.djvu
1. Generalities......Page all_19785_to_00314.cpc0041.djvu
2. Co-invariants......Page all_19785_to_00314.cpc0042.djvu
3. The Definition of H_* G......Page all_19785_to_00314.cpc0043.djvu
4. Topological Interpretation......Page all_19785_to_00314.cpc0044.djvu
5. Hopf\'s Theorems......Page all_19785_to_00314.cpc0049.djvu
6. Functoriality......Page all_19785_to_00314.cpc0056.djvu
7. The Homology of Amalgamated Free Products......Page all_19785_to_00314.cpc0057.djvu
Appendix. Trees and Amalgamations......Page all_19785_to_00314.cpc0060.djvu
0. Preliminaries on \\tensor_G and Hom_G......Page all_19785_to_00314.cpc0063.djvu
1. Definition of H_*(G,M) and H^*(G,M)......Page all_19785_to_00314.cpc0064.djvu
2. Tor and Ext......Page all_19785_to_00314.cpc0068.djvu
3. Extension and Co-extension of Scalars......Page all_19785_to_00314.cpc0070.djvu
4. Injective Modules......Page all_19785_to_00314.cpc0073.djvu
5. Induced and Co-induced Modules......Page all_19785_to_00314.cpc0075.djvu
6. Hi_* and H^* as Functors of the Coefficient Module......Page all_19785_to_00314.cpc0079.djvu
7. Dimension Shifting......Page all_19785_to_00314.cpc0082.djvu
8. H_* and H^* as Functors of Two Variables......Page all_19785_to_00314.cpc0086.djvu
9. The Transfer Map......Page all_19785_to_00314.cpc0088.djvu
10. Applications of the Transfer......Page all_19785_to_00314.cpc0091.djvu
1. Introduction......Page all_19785_to_00314.cpc0094.djvu
2. Split Extensions......Page all_19785_to_00314.cpc0095.djvu
3. The Classification of Extensions with Abelian Kernel......Page all_19785_to_00314.cpc0099.djvu
4. Application: p-Groups with a Cyclic Subgroup of Index p......Page all_19785_to_00314.cpc0105.djvu
5. Crossed Modules and H^3 (Sketch)......Page all_19785_to_00314.cpc0110.djvu
6. Extensions With Non-Abelian Kernel (Sketch)......Page all_19785_to_00314.cpc0112.djvu
1. The Tensor Product of Resolutions......Page all_19785_to_00314.cpc0115.djvu
2. Cross-products......Page all_19785_to_00314.cpc0116.djvu
3. Cup and Cap Products......Page all_19785_to_00314.cpc0117.djvu
4. Composition Products......Page all_19785_to_00314.cpc0122.djvu
5. The Pontryagin Product......Page all_19785_to_00314.cpc0125.djvu
6. Application: Calculation of the Homology of an Abelian Group......Page all_19785_to_00314.cpc0129.djvu
1. Introduction......Page all_19785_to_00314.cpc0136.djvu
2. Relative Homological Algebra......Page all_19785_to_00314.cpc0137.djvu
3. Complete Resolutions......Page all_19785_to_00314.cpc0139.djvu
4. Definition of \\hat{H}^*......Page all_19785_to_00314.cpc0142.djvu
5. Properties of \\hat{H}^*......Page all_19785_to_00314.cpc0144.djvu
6. Composition Products......Page all_19785_to_00314.cpc0150.djvu
7. A Duality Theorem......Page all_19785_to_00314.cpc0152.djvu
8. Cohomologically Trivial Modules......Page all_19785_to_00314.cpc0156.djvu
9. Groups with Periodic Cohomology......Page all_19785_to_00314.cpc0161.djvu
2. The Spectral Sequence of a Filtered Complex......Page all_19785_to_00314.cpc0169.djvu
3. Double Complexes......Page all_19785_to_00314.cpc0172.djvu
4. Example: The Homology of a Union......Page all_19785_to_00314.cpc0174.djvu
5. Homology of a Group with Coefficients in a Chain Complex......Page all_19785_to_00314.cpc0176.djvu
6. Example: The Hochschild-Serre Spectral Sequence......Page all_19785_to_00314.cpc0179.djvu
7. Equivariant Homology......Page all_19785_to_00314.cpc0180.djvu
8. Computation of d^1......Page all_19785_to_00314.cpc0183.djvu
9. Example: Amalgamations......Page all_19785_to_00314.cpc0186.djvu
10. Equivariant Tate Cohomology......Page all_19785_to_00314.cpc0188.djvu
1. Introduction......Page all_19785_to_00314.cpc0191.djvu
2. Cohomological Dimension......Page all_19785_to_00314.cpc0192.djvu
3. Serre\'s Theorem......Page all_19785_to_00314.cpc0198.djvu
4. Resolutions of Finite Type......Page all_19785_to_00314.cpc0199.djvu
5. Groups of Type FP_n......Page all_19785_to_00314.cpc0205.djvu
6. Groups of Type FP and FL......Page all_19785_to_00314.cpc0207.djvu
7. Topological Interpretation......Page all_19785_to_00314.cpc0213.djvu
8. Further Topological Results......Page all_19785_to_00314.cpc0218.djvu
9. Further Examples......Page all_19785_to_00314.cpc0221.djvu
10. Duality Groups......Page all_19785_to_00314.cpc0227.djvu
11. Virtual Notions......Page all_19785_to_00314.cpc0233.djvu
1. Ranks of Projective Modules: Introduction......Page all_19785_to_00314.cpc0238.djvu
2. The Hattori-Stallings Rank......Page all_19785_to_00314.cpc0239.djvu
3. Ranks Over Commutative Rings......Page all_19785_to_00314.cpc0243.djvu
4. Ranks Over Group Rings; Swan\'s Theorem......Page all_19785_to_00314.cpc0247.djvu
5. Consequences of Swan\'s Theorem......Page all_19785_to_00314.cpc0250.djvu
6. Euler Characteristics of Groups: The Torsion-Free Case......Page all_19785_to_00314.cpc0254.djvu
7. Extension to Groups with Torsion......Page all_19785_to_00314.cpc0257.djvu
8. Euler Characteristics and Number Theory......Page all_19785_to_00314.cpc0261.djvu
9. Integrality Properties of \\chi(\\Gamma)......Page all_19785_to_00314.cpc0265.djvu
10. Proof of Theorem 9.3; Finite Group Actions......Page all_19785_to_00314.cpc0266.djvu
11. The Fractional Part of \\chi(\\Gamma)......Page all_19785_to_00314.cpc0269.djvu
12. Acyclic Covers; Proof of Lemma 11.2......Page all_19785_to_00314.cpc0273.djvu
13. The p-Fractional Part of chi(\\Gamma)......Page all_19785_to_00314.cpc0274.djvu
14. A Formula for \\chi_Gamma(\\mathcal{A})......Page all_19785_to_00314.cpc0278.djvu
2. Complete Resolutions......Page all_19785_to_00314.cpc0281.djvu
3. Definition and Properties of \\hat{H}^*(\\Gamma)......Page all_19785_to_00314.cpc0285.djvu
4. Equivariant Farrell Cohomology......Page all_19785_to_00314.cpc0289.djvu
5. Cohomologically Trivial Modules......Page all_19785_to_00314.cpc0295.djvu
6. Groups with Periodic Cohomology......Page all_19785_to_00314.cpc0296.djvu
7. \\hat{H}^*(\\Gamma) and the Ordered Set of Finite Subgroups of \\Gamma......Page all_19785_to_00314.cpc0299.djvu
References......Page all_19785_to_00314.cpc0303.djvu
Notation Index......Page all_19785_to_00314.cpc0309.djvu
Index......Page all_19785_to_00314.cpc0311.djvu