Authors:
- Contains all of the material from the previous book, Buildings by K. S. Brown (a short, friendly, elementary introduction to the theory of buildings), and substantially revised, updated, new material
- Includes advanced content that is appropriate for more advanced students or for self-study, including two new chapters on the Moufang propert
- Introduces many new exercises and illustrations, as well as hints and solutions--including a separate, extensive solutions manual
- Thoroughly focuses on all three approachs to buildings, “old-fashioned," combinatorial (chamber systems), and metric so that the reader can learn all three or focus on only one
- Includes appendices on cell complexes, root systems and algebraic groups
- Request lecturer material: sn.pub/lecturer-material
Part of the book series: Graduate Texts in Mathematics (GTM, volume 248)
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Table of contents (15 chapters)
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Front Matter
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Back Matter
About this book
Reviews
From the reviews:
American Mathematical Society Mathematical Reviews MR2439729:
"The book under review ... is the first encyclopedic treatment of buildings made available in the literature, so that with writing this book the authors manage to close a serious gap in the mathematical literature: the non-existence of an easily accessible reference for buildings beyond an introduction.
In their introduction the authors state that it is their ``goal in this book to treat buildings from all three ... points of view [via the simplicial, the combinatorial, and the metric approach]. The various approaches complement one another and are useful. On the other hand, [the authors] recognize that some readers may prefer one particular viewpoint. [The authors] have therefore tried to create more than one path through the book so that, for example, the reader interested only in the combinatorial approach can learn the basics without having to spend too much time studying buildings as simplicial complexes.'' In the reviewer's opinion, the authors perfectly reach this goal and, moreover, manage to show that the theory of buildings and their applications are active, thriving, exciting and beautiful areas of mathematics. This book is very well written. The reviewer is sure that it will become a standard reference for buildings and remain one for a very long time.
... The main advantages of the combinatorial approach to buildings are that it is elementary and abstract and, hence, easily accessible. Since the simplicial and combinatorial approaches are equivalent..., one can always work with the one which is more suitable for one's own problems or more appealing to one's own taste. It is indeed one of the great achievements of this book to introduce both concepts simultaneously and to combine them in a natural way.
... Chapter 8 is extremely valuable for students and researchers interested in the theory of twin buildings, as it makes the theory... easily accessible. It is particularly important for the mathematical community that the folklore Theorem 8.27 has finally been recorded.
... Altogether, the book under review is a wonderful piece of work that will have many enthusiastic readers."
“This book is the first one which presents all of the different approaches to buildings alongside one another, and it does so in an accessible yet thorough manner which should prove extremely useful to anyone wishing to learn more about this interesting area of mathematics. The goal of presenting this introductory material in one place would be laudable enough. … this book is an extremely valuable addition to the mathematical literature. … it should also be an essential resource for experts in the area.” (Michael Bate, Zentralblatt MATH, Vol. 1214, 2011)
Authors and Affiliations
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Dept. Mathematics, University of Virginia, Charlottesville, U.S.A.
Peter Abramenko
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Dept. Neurobiology & Behavior, Cornell University, Ithaca, U.S.A.
Kenneth S. Brown
About the authors
Kenneth S. Brown has been a professor at Cornell since 1971. He received his Ph.D. in 1971 from MIT. He has published many works, including Buildings with Springer-Verlag in 1989, reprinted in 1998.
Peter Abramenko received his Ph.D. in 1987 from the University of Frankfurt, Germany. He held various academic positions afterwards, including a Heisenberg fellowship from 1998 until 2001. Since 2001, he is Associate Professor at the University of Virginia in Charlottesville. He has previously published Twin Buildings and Applications to S-Arithmetic Groups for the Lecture Notes in Mathematics series for Springer (1996).
Bibliographic Information
Book Title: Buildings
Book Subtitle: Theory and Applications
Authors: Peter Abramenko, Kenneth S. Brown
Series Title: Graduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-0-387-78835-7
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag New York 2008
Hardcover ISBN: 978-0-387-78834-0Published: 28 August 2008
Softcover ISBN: 978-1-4419-2701-9Published: 19 November 2010
eBook ISBN: 978-0-387-78835-7Published: 16 December 2008
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
Edition Number: 1
Number of Pages: XXII, 754
Number of Illustrations: 100 b/w illustrations
Topics: Group Theory and Generalizations, Algebraic Geometry, Topological Groups, Lie Groups