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 Buildings" includes 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.
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