Cohomology of Finite Groups

Alejandro Adem, R. James Milgram (Autoren)

Buch | Softcover

VIII, 324 Seiten

2010 | 2. Softcover reprint of hardcover 2nd ed. 2004
Springer Berlin (Verlag)
978-3-642-05785-4 (ISBN)

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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

I. Group Extensions, Simple Algebras and Cohomology.- II. Classifying Spaces and Group Cohomology.- III. Invariants and Cohomology of Groups.- IV. Spectral Sequences and Detection Theorems.- V. G-Complexes and Equivariant Cohomology.- VI. The Cohomology of the Symmetric Groups.- VII. Finite Groups of Lie Type.- VIII. Cohomology of Sporadic Simple Groups.- IX. The Plus Construction and Applications.- X. The Schur Subgroup of the Brauer Group.- References.

From the reviews of the second edition:

"This book is very different from other treatments since it emphasizes the computational aspects of the cohomology of finite groups with coefficients in a field. ... I say merely that each mathematician interested in algebra and topology should have a copy of this book on their shelf and make sure that their librarian gets one as well. Overall I thoroughly recommend this book and believe that it will be a useful book for introducing students to cohomological methods for groups." (Manuel Ladra Gonzalez, Zentralblatt MATH, Vol. 1061 (12), 2005)

Erscheint lt. Verlag	1.12.2010
Reihe/Serie	Grundlehren der mathematischen Wissenschaften
Zusatzinfo	VIII, 324 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	506 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Algebra • Algebraic K-Theory • algebraic topology • classifying spaces • cohomology • cohomology of groups • Group actions • Homological algebra • Homology • homotopy theory • K-theory
ISBN-10	3-642-05785-3 / 3642057853
ISBN-13	978-3-642-05785-4 / 9783642057854
Zustand	Neuware