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Cohomology Rings of Finite Groups - With an Appendix: Calculations of Cohomology Rings of Groups of Order Dividing 64 (Hardcover, 2003 ed.)
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Cohomology Rings of Finite Groups - With an Appendix: Calculations of Cohomology Rings of Groups of Order Dividing 64 (Hardcover, 2003 ed.)
Series: Algebra and Applications, 3
Expected to ship within 10 - 15 working days
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Group cohomology has a rich history that goes back a century or
more. Its origins are rooted in investigations of group theory and
num ber theory, and it grew into an integral component of algebraic
topology. In the last thirty years, group cohomology has developed
a powerful con nection with finite group representations. Unlike
the early applications which were primarily concerned with
cohomology in low degrees, the in teractions with representation
theory involve cohomology rings and the geometry of spectra over
these rings. It is this connection to represen tation theory that
we take as our primary motivation for this book. The book consists
of two separate pieces. Chronologically, the first part was the
computer calculations of the mod-2 cohomology rings of the groups
whose orders divide 64. The ideas and the programs for the
calculations were developed over the last 10 years. Several new
features were added over the course of that time. We had originally
planned to include only a brief introduction to the calculations.
However, we were persuaded to produce a more substantial text that
would include in greater detail the concepts that are the subject
of the calculations and are the source of some of the motivating
conjectures for the com putations. We have gathered together many
of the results and ideas that are the focus of the calculations
from throughout the mathematical literature."
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