Cohomology of Groups (Graduate Texts in Mathematics, No. 87)

As a second year graduate textbook, **Cohomology of Groups** introduces students to cohomology theory (involving a rich interplay between algebra and topology) with a minimum of prerequisites. No homological algebra is assumed beyond what is normally learned in a first course in algebraic topology. The basics of the subject are given (along with exercises) before the author discusses more specialized topics. Front Matter....Pages i-x Introduction....Pages 1-3 Some Homological Algebra....Pages 4-32 The Homology of a Group....Pages 33-54 Homology and Cohomology with Coefficients....Pages 55-85 Low-Dimensional Cohomology and Group Extensions....Pages 86-106 Products....Pages 107-127 Cohomology Theory of Finite Groups....Pages 128-160 Equivariant Homology and Spectral Sequences....Pages 161-182 Finiteness Conditions....Pages 183-229 Euler Characteristics....Pages 230-272 Farrell Cohomology Theory....Pages 273-294 Back Matter....Pages 295-309 Aimed at second year graduate students, this text introduces them to cohomology theory (involving a rich interplay between algebra and topology) with a minimum of prerequisites. No homological algebra is assumed beyond what is normally learned in a first course in algebraic topology, and the basics of the subject, as well as exercises, are given prior to discussion of more specialized topics. We collect here for ease of reference some terminology and results concerning chain complexes.