introduction to the 2009 edition
introduction
leitfaden
chapter 1 - chamber systems and examples
1. chamber systems
2. two examples of buildings
exercises
chapter 2 - coxeter complexes
1. coxeter groups and complexes
2. words and galleries
3. reduced words and homotopy
4. finite coxeter complexes
5. self-homotopy
exercises
chapter 3 - buildings
1. a definition of buildings
2. generalised m-gons - the rank 2 case
3. residues and apartments
exercises
chapter 4 - local properties and coverings
1. chamber systems of type m
2. coverings and the fundamental group
3. the universal cover
4. examples
exercises
chapter 5 - bn - pairs
1. tits systems and buildings
2. parabolic subgroups
exercises
chapter 6 - buildings of spherical type and root groups
1. some basic lemmas
2. root groups and the moufang property
3. commutator relations
4. moufang buildings - the general case
exercises 80
chapter 7 - a construction of buildings
1. blueprints
2. natural labellings of moufang buildings
3. foundations
exercises
chapter 8 - the classification of spherical buildings
1.a3 blueprints and foundations
2. diagrams with single bonds
3. c3 foundations
4. cn buildings for n > 4
5. tits diagrams and f4 buildings
6. finite buildings
exercises
chapter 9 - affine buildings I
1. affine coxeter complexes and sectors
2. the affine building an-1 (k,v)
3. the spherical building at infinity
4. the proof of (9.5)
exercises
chapter 10 - affine buildings II
1. apartment systems, trees and projective valuations
2. trees associated to walls and panels at infinity
3. root groups with a valuation
4. construction of an affine bn-pair
5. the classification
6. an application
exercises
chapter 11 - twin buildings
1. twin buildings and kac-moody groups
2. twin trees
3. twin apartments
4. an example: affine twin buildings
5. residues, rigidity, and proj.
6. 2-spherical twin buildings
7. the moufang property and root group data
8. twin trees again
appendix 1 - moufang polygons
1. the m-function
2. the natural labelling for a moufang plane
3. the non-existence theorem
appendix 2 - diagrams for moufang polygons
appendix 3 - non-discrete buildings
appendix 4 - topology and the steinberg representation
appendix 5 - finite coxeter groups
appendix 6 finite buildings and groups of lie type
bibliography
index of notation
index