Buildings
Published on 15. April 2013
Book
Paperback/Softback
VIII, 215 pages
978-1-4612-6987-8 (ISBN)
Description
For years I have heard about buildings and their applications to group theory. I finally decided to try to learn something about the subject by teaching a graduate course on it at Cornell University in Spring 1987. This book is based on the not es from that course. The course started from scratch and proceeded at a leisurely pace. The book therefore does not get very far. Indeed, the definition of the term "building" doesn't even appear until Chapter IV. My hope, however, is that the book gets far enough to enable the reader to tadle the literat ure on buildings, some of which can seem very forbidding. Most of the results in this book are due to J. Tits, who originated the the ory of buildings. The main exceptions are Chapter I (which presents some classical material), Chapter VI (which prcsents joint work of F. Bruhat and Tits), and Chapter VII (which surveys some applications, due to var ious people). It has been a pleasure studying Tits's work; I only hope my exposition does it justice.
More details
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Professional/practitioner
Illustrations
VIII, 215 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 13 mm
Weight
353 gr
ISBN-13
978-1-4612-6987-8 (9781461269878)
DOI
10.1007/978-1-4612-1019-1
Schweitzer Classification
Other editions
Person
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).
Content
I. Finite Reflection Groups.- II. Abstract Reflection Groups.- III. Coxeter Complexes.- IV. Buildings.- V. Buildings and Groups.- VI. Euclidean Buildings.- VII. Applications to Group Cohomology.- Suggestions for Further Reading.- References.- Notation Index.