Über den Autor
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).
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.
This book treats Jacques Tit's beautiful theory of buildings, making that theory accessible to readers with minimal background. It covers all three approaches to buildings, so that the reader can choose to concentrate on one particular approach. Beginners can use parts of the new book as a friendly introduction to buildings, but the book also contains valuable material for the active researcher.
This book is suitable as a textbook, with many exercises, and it may also be used for self-study.
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