Buildings: Theory and Applications

Peter Abramenko and Kenneth S. Brown
Graduate Texts in Mathematics, Vol. 248
Springer, New York, 2008. xxii+747 pp.
ISBN: 978-0-387-78834-0

Overview (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.

Further information

The authors

Peter Abramenko
Department of Mathematics
University of Virginia
Charlottesville, VA 22904

Ken Brown
Department of Mathematics
Cornell University
Ithaca, NY 14853


We will maintain a cumulative list of corrections. If you find errors (typographical or otherwise), please notify one or both authors.

The old book

By arrangement with the publisher, a scanned copy of Buildings by Kenneth S. Brown (published by Springer in 1989) is available for free download [pdf file, djvu file].