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Cohomology rings of finite groups : with an appendix, calculations of cohomology rings of groups of order dividing 64

Author: J F Carlson
Publisher: Dordrecht ; Boston : Kluwer Academic Publishers, ©2003.
Series: Algebras and applications, v. 3.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

Group cohomology has a rich history that goes back a century or more. Unlike the early applications which were primarily concerned with cohomology in low degrees, the in- teractions with  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: J F Carlson
ISBN: 1402015259 9781402015250
OCLC Number: 53099072
Description: xv, 776 pages ; 25 cm.
Contents: Preface. Acknowledgements. 1: Homological Algebra. 1. Introduction. 2. Complexes and Sequences. 3. Projective and Injective Models. 4. Resolutions. 5. Ext. 6. Tensor Products and Tor. 2: Group Algebras. 1. Introduction. 2. Duality and Tensor Products. 3. Induction and Restriction. 4. Radicals, Socles and Projective Modules. 5. Degree Shifting. 6. The Stable Category. 7. Group Cohomology and Change of Coefficients. 3: Projective Resolutions. 1. Introduction. 2. Minimal Resolutions. 3. The Bar Resolution. 4. Applications to Low Dimensional Cohomology. 5. Restrictions, Inflations and Transfers. 4: Cohomology Products. 1. Introduction. 2. Yoneda Splices and Compositions of Chain Maps. 3. Products and Group Algebras. 4. Restriction, Inflation and Transfer. 5. Cohomology Ring Computations. 6. Shifted Subgroups and Restrictions. 7. Automorphisms and Cohomology. 5: Spectral Sequences. 1. Introduction. 2. The Spectral Sequence of a Biocomplex. 3. Products. 4. The Lyndon-Hochschild-Serre Spectral Sequence. 5. Extension Classes. 6. Minimal Resolutions and Convergence. 7. Exact Couples and the Bockstein Spectral Sequence. 6: Norms and the Cohomology of Wreath Products. 1. Introduction. 2. Wreath Products. 3. The Norm Map. 4. Examples and Applications. 5. Finite Generation of Cohomology. 7: Steenrod Operations. 1. Introduction. 2. The Steenrod Algebra and Modules. 3. The Steenrod Operations on Cohomology. 4. Cohomology and Modules Over the Steenrod Algebra. 5. The Cohomology of Extraspecial 2-Groups. 6. The Cohomology of Extraspecial p-Groups. 7. Serre's Theorem on the Vanishing of Bocksteins. 8: Varieties and Elementary Abelian Subgroups. 1. Introduction. 2. Filtrations on Modules. 3. Vanishing Products of Cohomology Elements. 4. Minimal Primes in Cohomology Rings. 5. The Stratification Theorem. 9: Cohomology Rings of Modules. 1. Introduction. 2. Generalized Bocksteins Over Elementary Abelian Groups. 3. Rank Varieties and Cohomology Rings Over Elementary Abelian Groups. 4. The Cohomological Support Variety of a Module. 5. Equating the Rank and Cohomological Support Varieties. 6. The Tensor Product Theorem. 7. Properties of the Cohomological Support Varieties. 10: Complexity and Multiple Complexes. 1. Introduction. 2. Notes on Dimension and Rates of Growth. 3. Complexity of Modules. 4. Varieties for Modules with Other Coefficient Rings. 5. Projective Resolutions as Multiple Complexes. 11: Duality Complexes. 1. Introduction. 2. Gaps in Cohomology. 3. Poincare Duality Complexes. 4. Differentials in the HSS. 5. Cohen Macaulay Cohomology Rings. 6. Further Considerations. 12: Transfers, Depth and Detection. 1. Introduction. 2. Notes
Series Title: Algebras and applications, v. 3.
Responsibility: Jon F. Carlson [and others].
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From the reviews:"The cohomology of groups was developed to be ... a powerful tool in the study of group representations. ... Some other books concerning the cohomology of finite groups have Read more...

 
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