Buildings

1. Front Matter

   Pages i-viii

   PDF

2. Finite Reflection Groups

   • Kenneth S. Brown

   Pages 1-32

3. Abstract Reflection Groups

   • Kenneth S. Brown

   Pages 33-57

4. Coxeter Complexes

   • Kenneth S. Brown

   Pages 58-75

5. Buildings

   • Kenneth S. Brown

   Pages 76-98

6. Buildings and Groups

   • Kenneth S. Brown

   Pages 99-138

7. Euclidean Buildings

   • Kenneth S. Brown

   Pages 139-182

8. Applications to Group Cohomology

   • Kenneth S. Brown

   Pages 183-205

9. Back Matter

   Pages 206-215

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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.

• DEX
• Finite
• Group theory
• Microsoft Access
• Scratch
• cohomology
• geometry
• group
• homology
• mathematics
• minimum
• reflection
• topology

• Department of Mathematics, Cornell University, Ithaca, USA

  Kenneth S. Brown

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