Twin Buildings and Applications to S-Arithmetic Groups

This volume is aimed at mathematicians and advanced students interested in buildings, groups and their interplay. Its first part, which presupposes a good knowledge of ordinary buildings, looks at the theory of twin buildings, discusses its group-theoretic background (twin BN-pairs), investigates geometric aspects of twin buidings and applies them to determine finiteness properties of certain S-arithmetic groups. This application depends on topological properties of some subcomplexes of spherical buildings. The background of this problem, some examples and the complete solution for all "sufficiently large" classical buildings are covered in detail in the second part of the book.