Buildings. (English) Zbl 0715.20017

New York etc.: Springer-Verlag. viii, 215 p. DM 78.00 (1989).
This book gives a good introduction to the theory of buildings. It gives complete proofs and plenty of exercises and examples. Most of the results can be found in the works of Tits (usually in French). Chapter VII gives a survey of some applications. There it is shown how the construction of a building that provides a p-adic analogue of a symmetric space can be used to generalize results on the cohomology of arithmetic groups to the case of S-arithmetic groups.
Reviewer: F.Levstein


20E42 Groups with a \(BN\)-pair; buildings
20G10 Cohomology theory for linear algebraic groups
20-02 Research exposition (monographs, survey articles) pertaining to group theory
51E24 Buildings and the geometry of diagrams
51F15 Reflection groups, reflection geometries