Twin Buildings and Applications to S-Arithmetic Groups

Peter Abramenko (auth.)3540619739, 9783540619734

This book is addressed to mathematicians and advanced students interested in buildings, groups and their interplay. Its first part introduces – presupposing good knowledge of ordinary buildings – the theory of twin buildings, discusses its group-theoretic background (twin BN-pairs), investigates geometric aspects of twin buildings 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.

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Table of contents :
Introduction….Pages 1-10
Groups acting on twin buildings….Pages 11-55
Homotopy properties of ∮Δ 0 (a)∮….Pages 56-106
Finiteness properties of classical F q over F q [t]….Pages 107-114