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Buildings: Theory and Applications

Buildings: Theory and Applications
Catalogue Information
Field name Details
Dewey Class 512.2
Title Buildings (EB) : Theory and Applications / by Peter Abramenko, Kenneth S. Brown.
Author Abramenko, Peter
Added Personal Name Brown, Kenneth S.
Other name(s) SpringerLink (Online service)
Publication New York, NY : Springer , 2008.
Physical Details XXII, 754p. 100 illus. : online resource.
Series Graduate texts in mathematics 0072-5285 ; ; 248
ISBN 9780387788357
Summary Note 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.:
Contents note Preface -- Introduction -- Finite Reflection Groups -- Coxeter Groups -- Coxeter Complexes -- Buildings as Chamber Complexes -- Buildings as W-Metric Spaces -- Buildings and Groups -- Root Groups and the Moufang Property -- Moufang Twin Buildings and RGD-Systems -- The Classification of Spherical Buildings -- Euclidean and Hyperbolic Reflection Groups -- Euclidean Buildings -- Buildings as Metric Spaces -- Applications to the Cohomology of Groups -- Other Applications -- Cell Complexes -- Root Systems -- Algebraic Groups.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
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