Buildings (eBook)

Theory and Applications

Peter Abramenko, Kenneth S. Brown (Autoren)

eBook Download: PDF

2008 | 2008. Auflage
XXII, 754 Seiten
Springer New York (Verlag)
978-0-387-78835-7 (ISBN)

Infos

Covering all three approaches to Jacques Tits's beautiful theory of buildings, this accessible volume is suitable as a textbook introduction to the subject as well as a self-study text for researchers. It contains numerous exercises.

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This text started out as a revised version of Buildings by the second-named author [53], but it has grown into a much more voluminous book. The earlier book was intended to give a short, friendly, elementary introduction to theory, accessible to readers with a minimal background.Moreover, it approached buildings from only one point of view, sometimes called the "e;old-fashioned"e; approach: A building is a simplicial complex with certain properties. The current book includes all the material of the earlier one, but we have added a lot. In particular, we have included the "e;modern"e; (or "e;W-metric"e;) approach to buildings, which looks quite different from the old-fashioned approach but is equivalent to it. This has become increasingly important in the theory and applications of buildings. We have also added a thorough treatment of the Moufang property, which occupies two chapters. And we have added many new exercises and illustrations. Some of the exercises have hints or solutions in the back of the book. A more extensive set of solutions is available in a separate solutions manual, which may be obtained from Springer's Mathematics Editorial Department. We have tried to add the new material in such a way that readers who are content with the old-fashioned approach can still get an elementary treatment of it by reading selected chapters or sections. In particular, many readers will want to omit the optional sections (marked with a star). The introduction below provides more detailed guidance to the reader.

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).

Inhalt

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.

Produkt-Details

• Erscheint lt. Verlag: 16.12.2008
• Reihe/Serie: Graduate Texts in Mathematics
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Schlagworte: cohomology • combinatorial approach • Coxeter • euclidean buildings • Homology • metric approach • Moufang property • simplicial approach
• ISBN-10: 0-387-78835-2 / 0387788352
• ISBN-13: 978-0-387-78835-7 / 9780387788357