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Books > Science & Mathematics > Mathematics > Topology > Algebraic topology
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Cohomology of Finite Groups (Paperback, Softcover reprint of hardcover 2nd ed. 2004)
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Cohomology of Finite Groups (Paperback, Softcover reprint of hardcover 2nd ed. 2004)
Series: Grundlehren der mathematischen Wissenschaften, 309
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Some Historical Background This book deals with the cohomology of
groups, particularly finite ones. Historically, the subject has
been one of significant interaction between algebra and topology
and has directly led to the creation of such important areas of
mathematics as homo logical algebra and algebraic K-theory. It
arose primarily in the 1920's and 1930's independently in number
theory and topology. In topology the main focus was on the work
ofH. Hopf, but B. Eckmann, S. Eilenberg, and S. MacLane (among
others) made significant contributions. The main thrust of the
early work here was to try to understand the meanings of the low
dimensional homology groups of a space X. For example, if the
universal cover of X was three connected, it was known that H2(X;
A. ) depends only on the fundamental group of X. Group cohomology
initially appeared to explain this dependence. In number theory,
group cohomology arose as a natural device for describing the main
theorems of class field theory and, in particular, for describing
and analyzing the Brauer group of a field. It also arose naturally
in the study of group extensions, N"
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