CHAPTER 20

Applications of Buildings

Jürgen ROHLFS

Katholische Universität Eichstätt, Mathematisch-Geographische Fakultät,
Ostenstr. 26--28, D-85072 Eichstätt, Germany

Tony A. SPRINGER

Universiteit Utrecht, Mathematisch Instituut, Budapestlaan 6,
Postbus 80.010, NL-3508 TA Utrecht, The Netherlands

Contents

Introduction

1. The spherical building of a reductive group

2. Topological properties, the Steinberg representation

3. Affine buildings

4. The Borel--Serre compactification

5. An application to cohomology of S-arithmetic groups

6. Covolumes of arithmetic groups

7. Applications of buildings in differential geometry

References