Schesler, Eduard: The Sigma-Invariants of S-arithmetic subgroups of Borel groups. 2020
Inhalt
- Dedication
- Abstract
- Zusammenfassung
- Acknowledgments
- Contents
- 1 Introduction
- 2 Basic notions
- 2.1 Metric spaces
- 2.2 Polytopes and polyhedra
- 2.3 Topology
- 2.4 Coxeter complexes and buildings
- 2.5 The spherical building at infinity
- 2.6 The opposition complex
- 2.7 -invariants
- 3 Deconstructing subcomplexes of Coxeter complexes
- 4 The positive direction in top dimension
- 5 The negative direction in top dimension
- 6 Convex functions on CAT(0)-spaces
- 7 Parabolic buildings
- 7.1 Apartments in the parabolic building
- 7.2 A subbuilding of X
- 7.3 A new structure for the extended Levi building
- 8 The geometric main result
- 8.1 Retractions in parabolic buildings
- 8.2 Reduction of the horizontal dimension
- 8.3 The geometric main result
- 9 Chevalley groups, Borel groups, and their S-arithmetic subgroups
- 9.1 Background on Lie algebras
- 9.2 Chevalley groups and their associated subgroups
- 9.3 From Chevalley groups to RGD-systems and BN-pairs
- 9.4 From valued root group data to BN-pairs
- 9.5 From BN-pairs to buildings
- 9.6 A metric for the buildings
- 9.7 The case of p-adic valuations
- 10 -invariants of S-arithmetic Borel groups
- 10.1 Finiteness properties of the stabilizers
- 10.2 Cocompactness of the action
- 10.3 The structure of the Character sphere
- 10.4 Extending characters to height functions
- 10.5 Sigma invariants of S-arithmetic Borel groups
- Alphabetical Index
- Bibliography