Overview

This text offers comprehensive coverage of group cohomology, from introductory material through the most recent developments in the field. The primary motivation for the book is the interaction of group cohomology with representation theory, especially the geometry of support varieties over cohomology rings. The appendices, comprising computer calculations of the mod-2 cohomology rings of the groups whose orders divide 64, provide information useful for further developments in the field. A feature of this text is that it includes the concepts that are the subject of the calculations and are the source of some of the motivating conjectures for the computations. The programs for computing the cohomology rings were executed in the MAGMA computer algebra language. The text is a useful resource for researchers in group cohomology and related disciplines. In addition, it could be used as a text for an advanced graduate class or a graduate seminar.

Full Product Details

Author:   Jon F. Carlson ,  L. Townsley ,  Luís Valero-Elizondo ,  Mucheng Zhang
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   2003 ed.
Volume:   3
Dimensions:   Width: 15.50cm , Height: 4.20cm , Length: 23.50cm
Weight:   2.830kg
ISBN:  

9781402015250

ISBN 10:   1402015259
Pages:   776
Publication Date:   31 October 2003
Audience:   Professional and scholarly ,  College/higher education ,  Professional & Vocational ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1. Homological Algebra.- 2. Group Algebras.- 3. Projective Resolutions.- 4. Cohomology Products.- 5. Spectral Sequences.- 6. Norms and the Cohomology of Wreath Products.- 7. Steenrod Operations.- 8. Varieties and Elementary Abelian Subgroups.- 9. Cohomology Rings of Modules.- 10. Complexity and Multiple Complexes.- 11. Duality Complexes.- 12. Transfers, Depth and Detection.- 13. Subgroup Complexes.- 14. Computer Calculations and Completion Tests.- Appendices: Calculations of the Cohomology Rings of Groups of Order Dividing 64.- A— Notation and References.- B— Groups of Order 8.- C— Groups of Order 16.- D— Groups of Order 32.- E— Groups of Order 64.- F— Tables of Krull Dimension and Depth.- G— Tables of Hilbert / Poincaré Series.- References.

Reviews

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 appeared, but they are at least ten years old, and the computational tools that have been developed since then, make this book to be really valuable for both professionals and students. ... This book is almost self-contained and it is very useful ... for all of those that are using the cohomology instruments in their work. (Viorel Mihai Gontineac, Zentralblatt MATH, Vol. 1056 (7), 2005)

From the reviews: <p> The cohomology of groups was developed to be a ] a powerful tool in the study of group representations. a ] Some other books concerning the cohomology of finite groups have appeared, but they are at least ten years old, and the computational tools that have been developed since then, make this book to be really valuable for both professionals and students. a ] This book is almost self-contained and it is very useful a ] for all of those that are using the cohomology instruments in their work. (Viorel Mihai Gontineac, Zentralblatt MATH, Vol. 1056 (7), 2005)

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 appeared, but they are at least ten years old, and the computational tools that have been developed since then, make this book to be really valuable for both professionals and students. ... This book is almost self-contained and it is very useful ... for all of those that are using the cohomology instruments in their work. (Viorel Mihai Gontineac, Zentralblatt MATH, Vol. 1056 (7), 2005)

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