In recent years cube complexes have become a cornerstone topic of geometric group theory and have proven to be a powerful tool in other areas, such as low dimensional topology, phylogenetic trees or in the context of optimization problems.
This book covers a wide variety of algebraic and geometric properties of cube complexes and the groups acting on them. The content ranges from basic properties of metric spaces, notions of non-positive curvature, Gromov's link condition and the svarc-Milnor theorem to advanced material such as the cubulation of half-space systems and the Roller boundary, the construction of cube complexes associated with Coxeter groups, and the Tits alternative for cubical groups.
Being the first self-contained, comprehensive introduction to cube complexes this book serves as an entry point for researchers interested in the subject. The material is accessible to advanced undergraduate and graduate students. The text is illustrated with many figures and examples and comes with a large collection of exercises.
Inhaltsverzeichnis
- 1. Introduction. - 2. Metric Spaces Meet Groups. - 3. Non-positive Curvature. - 4. Cube Complexes and Gromov s Link Condition. - 5. Hyperplanes and Half-Spaces. - 6. Cubulating Coxeter Groups. - 7. A Panoramic Tour.
