Buildings: Theory and Applications
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 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.
From the Back Cover This book treats Jacques Tits's beautiful theory of buildings, making that theory accessible to readers with minimal background. It includes all the material of the earlier book Buildings by the second-named author, published by Springer-Verlag in 1989, which gave an introduction to buildings from the classical (simplicial) point of view. This new book also includes two other approaches to buildings, which nicely complement the simplicial approach: On the one hand, buildings may be viewed as abstract sets of chambers with a Weyl-group-valued distance function; this point of view has become increasingly important in the theory and applications of buildings. On the other hand, buildings may be viewed as metric spaces. Beginners can still use parts of the new book as a friendly introduction to buildings, but the book also contains valuable material for the active researcher. There are several paths through the book, so that readers may choose to concentrate on one particular approach. The pace is gentle in the elementary parts of the book, and the style is friendly throughout. All concepts are well motivated. There are thorough treatments of advanced topics such as the Moufang property, with arguments that are much more detailed than those that have previously appeared in the literature. This book is suitable as a textbook, with many exercises, and it may also be used for self-study.