Book Search:  

 

 
Google full text of our books:

bookjacket

The Structure of Spherical Buildings
Richard M. Weiss

Hardcover | 2004 | $67.50 / £46.95 | ISBN: 9780691117331
144 pp. | 6 x 9 | 16 line illus. | SHOPPING CART

Reviews | Table of Contents
Chapter 1[PDF] pdf-icon

Google full text of this book:
 

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.

Review:

"Richard M. Weiss's book is an extremely valuable addition to the literature."--Kenneth S. Brown, Bulletin of the American Mathematical Society

Endorsement:

"This is the best currently available introduction to the theory of buildings. And it brings the reader to a very important theorem in the theory of spherical buildings. Moreover, it is very carefully written: obviously the author spent quite some time arranging the different results in the right order, which isn't a straightforward task. As for explaining the really hard part of the classification of spherical buildings, this book is a perfect complement to the existing literature."--Hendrik Van Maldeghem, Ghent University

"This book makes an important contribution to the theory of buildings, developing some material in ways that were unavailable until recently. Weiss is an expert in the field who has produced a book that will be useful to anyone learning the subject."--Mark A. Ronan, University of Illinois at Chicago and University College London

Table of Contents:

Preface ix
Chapter 1. Chamber Systems 1
Chapter 2. Coxeter Groups 9
Chapter 3. Roots 17
Chapter 4. Reduced Words 27
Chapter 5. Opposites 33
Chapter 6. 2-Interiors 41
Chapter 7. Buildings 47
Chapter 8. Apartments 61
Chapter 9. Spherical Buildings 73
Chapter 10. Extensions of Isometries 81
Chapter 11. The Moufang Property 91
Chapter 12. Root Group Labelings 117
References 131
Index 133

Other Princeton books authored or coauthored by Richard M. Weiss:

Subject Area:

VISIT OUR MATH WEBSITE

Shopping Cart:

  • For hardcover/paperback orders:

    For hardcover/paperback orders in the United States, Canada, Latin America, Asia, and Australia

    Hardcover: $67.50 ISBN: 9780691117331

    For hardcover/paperback orders in Europe, Africa, the Middle East, and India

    Hardcover: £46.95 ISBN: 9780691117331

    Add to shopping cart

    Prices subject to change without notice

    File created: 9/19/2014

Questions and comments to: webmaster@press.princeton.edu
Princeton University Press

New Book E-mails
New In Print
PUP Blog
Videos/Audios
Princeton APPS
Sample Chapters
Subjects
Series
Catalogs
Princeton Legacy Library
Textbooks
Media/Reviewers
Class Use
Rights/Permissions
Ordering
Recent Awards
Princeton Shorts
Freshman Reading
PUP Europe
About Us
Contact Us
Links
F.A.Q.
MATH SITE
PUP Home


Bookmark and Share
Send me emails
about new books in:
Mathematics
More Choices
Email:
Country:
Name: