Kenneth S. Brown - Böcker

The earlier book was intended to give a short, friendly, elementary introduction to theory, accessible to readers with a minimal background.Moreover, it approached buildings from only one point of view, sometimes called the “old-fashioned” approach: A building is a simplicial complex with certain properties.

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.

This book gives an introduction to Jacques Tit's theory of buildings, a subject in which there is a rich interplay between group theory and geometry. The book starts from scratch, with a discussion of finite reflection groups, and takes the reader to the literature on buildings. The prerequisites are kept to a minimum, and careful attention is paid to motivating new concepts that are introduced. The book should be accessible to any mathematics graduate student who knows very little group theory and topology.

This text started out as a revised version of Buildings by the second-named author [53], but it has grown into a much more voluminous book. The earlier book was intended to give a short, friendly, elementary introduction to theory, accessible to readers with a minimal background.Moreover, it approached buildings from only one point of view, sometimes called the “old-fashioned” approach: A building is a simplicial complex with certain properties. The current book includes all the material of the earlier one, but we have added a lot. In particular, we have included the “modern” (or “W-metric”) approach to buildings, which looks quite different from the old-fashioned approach but is equivalent to it. This has become increasingly important in the theory and applications of buildings. We have also added a thorough treatment of the Moufang property, which occupies two chapters. And we have added many new exercises and illustrations. Some of the exercises have hints or solutions in the back of the book. A more extensive set of solutions is available in a separate solutions manual, which may be obtained from Springer’s Mathematics Editorial Department. We have tried to add the new material in such a way that readers who are content with the old-fashioned approach can still get an elementary treatment of it by reading selected chapters or sections. In particular, many readers will want to omit the optional sections (marked with a star). The introduction below provides more detailed guidance to the reader.