| Preface |
| Acknowledgements |
| Homological Algebra / 1： |
| Introduction |
| Complexes and Sequences / 2： |
| Projective and Injective Models / 3： |
| Resolutions / 4： |
| Ext / 5： |
| Tensor Products and Tor / 6： |
| Group Algebras |
| Duality and Tensor Products |
| Induction and Restriction |
| Radicals, Socles and Projective Modules |
| Degree Shifting |
| The Stable Category |
| Group Cohomology and Change of Coefficients / 7： |
| Projective Resolutions |
| Minimal Resolutions |
| The Bar Resolution |
| Applications to Low Dimensional Cohomology |
| Restrictions, Inflations and Transfers |
| Cohomology Products |
| Yoneda Splices and Compositions of Chain Maps |
| Products and Group Algebras |
| Restriction, Inflation and Transfer |
| Cohomology Ring Computations |
| Shifted Subgroups and Restrictions |
| Automorphisms and Cohomology |
| Spectral Sequences |
| The Spectral Sequence of a Biocomplex |
| Products |
| The Lyndon-Hochschild-Serre Spectral Sequence |
| Extension Classes |
| Minimal Resolutions and Convergence |
| Exact Couples and the Bockstein Spectral Sequence |
| Norms and the Cohomology of Wreath Products |
| Wreath Products |
| The Norm Map |
| Examples and Applications |
| Finite Generation of Cohomology |
| Steenrod Operations |
| The Steenrod Algebra and Modules |
| The Steenrod Operations on Cohomology |
| Cohomology and Modules Over the Steenrod Algebra |
| The Cohomology of Extraspecial 2-Groups |
| The Cohomology of Extraspecial p-Groups |
| Serre's Theorem on the Vanishing of Bocksteins |
| Varieties and Elementary Abelian Subgroups / 8： |
| Filtrations on Modules |
| Vanishing Products of Cohomology Elements |
| Minimal Primes in Cohomology Rings |
| The Stratification Theorem |
| Cohomology Rings of Modules / 9： |
| Generalized Bocksteins Over Elementary Abelian Groups |
| Rank Varieties and Cohomology Rings Over Elementary Abelian Groups |
| The Cohomological Support Variety of a Module |
| Equating the Rank and Cohomological Support Varieties |
| The Tensor Product Theorem |
| Properties of the Cohomological Support Varieties |
| Complexity and Multiple Complexes / 10： |
| Notes on Dimension and Rates of Growth |
| Complexity of Modules |
| Varieties for Modules with Other Coefficient Rings |
| Projective Resolutions as Multiple Complexes |
| Duality Complexes / 11： |
| Gaps in Cohomology |
| PoincarF Duality Complexes |
| Differentials in the HSS |
| Cohen Macaulay Cohomology Rings |
| Further Considerations |
| Transfers, Depth and Detection / 12： |
| Notes on Depth and Associated Primes |
| Depth and the p-Rank of the Center |
| Varieties and Transfers |
| Detection and Depth-Essential Cohomology |
| Special Cases |
| Associated Primes in Cohomology |
| Unstable Modules |
| Subgroup Complexes / 13： |
| Posets of Subgroups and Cell Complexes |
| Homotopy Equivalences and Equivariance |
| Complexes of Posets of Finite Groups |
| The Bouc Complex |
| Applications to Cohomology |
| Decompositions of Molecules |
| Additional Remarks |
| Cohomology Compositions |
| Computer Calculations and Completion Tests / 14： |
| The Visual Cohomology Ring: Generators and Relations |
| Resolutions, Maps and Homogeneous Parameters |
| Tests for Completion |
| Two Special Cases |
| Appendices: Calculations of the Cohomology Rings of Groups of Order Dividing 64 / J.F. Carlson ; L. Valero-Elizondo ; Mucheng Zhang |
| Notation and References / A： |
| Groups of Order 8 / B： |
| Groups of Order 16 / C： |
| Groups of Order 32 / D： |
| Groups of Order 64 / E： |
| Tables of Krull Dimension and Depth / F： |
| Tables of Hilbert/PoincarF Series / G： |
| References |
| Index |
図書
