Buildings: Theory and Applications [Hardcover]

This book treats Jacques Tit's beautiful theory of buildings, making that theory accessible to readers with minimal background. It covers all three approaches to buildings, so that the reader can choose to concentrate on one particular approach. Beginners can use parts of the new book as a friendly introduction to buildings, but the book also contains valuable material for the active researcher.

This book is suitable as a textbook, with many exercises, and it may also be used for self-study.

Covering all three approaches to Jacques Tits's beautiful theory of buildings, this accessible volume is suitable as a textbook introduction to the subject as well as a self-study text for researchers. It contains numerous exercises.

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 bookwasintendedtogiveashort,friendly,elementaryintroductiontothet- ory,accessibletoreaderswithaminimalbackground.Moreover,itapproached 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 di?erent from the old-fashioned - proach but is equivalent to it. This has become increasingly important in the theory and applications of buildings. We have also added a thorough tre- ment 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 ava- able in a separate solutions manual, which may be obtained from Springers Mathematics Editorial Department. We have tried to add the new material in such a way that readers who als›