Inhalt

•  
   Introduction
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  Main results
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   Wagoner complexes
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   Homological stability
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   Homological stability results
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   The construction of a relative spectral sequence
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   Lattices in two-dimensional affine buildings
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   Buildings of type ~A2
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   Buildings of type ~C2
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  Basic geometric concepts
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   Simplicial complexes
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   Non-positive curvature
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   Metric polyhedral complexes
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   Buildings
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  Coxeter complexes
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   Coxeter groups
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   Coxeter complexes
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   Roots
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   The canonical linear representation
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   Spherical Coxeter complexes
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   Affine Coxeter complexes
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  Buildings
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   The definition of buildings
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   Moufang spherical buildings
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   Metrics on buildings
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   Affine buildings
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  Groups acting on buildings
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   Strongly transitive actions and Tits systems
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   Groups of Kac-Moody type
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   Root data with valuations
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  Examples of buildings and classical groups
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   Generalised polygons
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   The spherical buildings of type An and linear groups
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   The spherical buildings of type Cn and unitary groups
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   Two-dimensional affine buildings
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  Group homology
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   Homological algebra
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  Group homology
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   Definition
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   Interpretations of group homology
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   Basic results
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   Relative group homology
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   Homological stability
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   Algebraic K-theory
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  Spectral sequences
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   The definition of spectral sequences
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   The spectral sequence associated to a filtered chain complex
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   The spectral sequence associated to a filtered topological space
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   The spectral sequences associated to a double complex
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   Equivariant homology
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   The Lyndon/Hochschild-Serre spectral sequence
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  Complexes of groups
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   Small categories without loops
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   Complexes of groups
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   Developability and non-positive curvature
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   Presentations by group actions
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  Wagoner complexes
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   The definition of Wagoner complexes
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   Simple properties of Wagoner complexes
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   The Steinberg group
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   Homotopy groups of Wagoner complexes
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   The connection to algebraic K-theory
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   Affine Wagoner complexes
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  Homological stability
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  Relative spectral sequences
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   Relative spectral sequences associated to tensor complexes
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   The relative Lyndon/Hochschild-Serre spectral sequence
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  The opposition complex and a relative spectral sequence
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   The opposition complex
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   A filtration
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   The relative spectral sequence
•  
  Homological stability
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   General linear groups
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   Special linear groups
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   Unitary groups
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  Lattices in buildings
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   Lattices in automorphism groups of polyhedral complexes
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  Complexes of groups with generalised polygons as local developments
•  
   Projective planes
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   Generalised quadrangles
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   A local complex of groups construction
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  Lattices in buildings of type ~A2
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   A general construction of panel-regular lattices in ~A2-buildings
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   The classification of panel-regular lattices
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   Lattices generated by cyclic Singer groups
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   Spheres of radius two
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  Lattices in buildings of type ~C2
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   Lattices acting regularly on two types of panels
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   Lattices acting regularly on one type of panel
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   Property (T)
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  Group homology of lattices
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   Group homology of lattices in buildings of type ~A2
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   Group homology of lattices in buildings of type ~C2
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   Open problems
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   Coxeter diagrams
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   Bibliography