The Structure of Spherical Buildings

by Weiss, Richard M.

• ISBN13: 9780691117331
• ISBN10: 0691117330
• Format: Hardcover
• Copyright: 2004-01-05
• Publisher: Princeton Univ Pr

Summary

This book provides a clear and authoritative introduction to the theory of buildings, a topic of central importance to mathematicians interested in the geometric aspects of group theory. Its detailed presentation makes it suitable for graduate students as well as specialists. Richard Weiss begins with an introduction to Coxeter groups and goes on to present basic properties of arbitrary buildings before specializing to the spherical case. Buildings are described throughout in the language of graph theory. The Structure of Spherical Buildingsincludes a reworking of the proof of Jacques Tits's Theorem 4.1.2. upon which Tits's classification of thick irreducible spherical buildings of rank at least three is based. In fact, this is the first book to include a proof of this famous result since its original publication. Theorem 4.1.2 is followed by a systematic study of the structure of spherical buildings and their automorphism groups based on the Moufang property. Moufang buildings of rank two were recently classified by Tits and Weiss. The last chapter provides an overview of the classification of spherical buildings, one that reflects these and other important developments.

Table of Contents

Preface	ix
Chamber Systems	1	(8)
Coxeter Groups	9	(8)
Roots	17	(10)
Reduced Words	27	(6)
Opposites	33	(8)
2-Interiors	41	(6)
Buildings	47	(14)
Apartments	61	(12)
Spherical Buildings	73	(8)
Extensions of Isometries	81	(10)
The Moufang Property	91	(26)
Root Group Labelings	117	(14)
References	131	(2)
Index	133