CAT(0) Cube Complexes

Beschreibung

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 Švarc–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.
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 Švarc–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.
First self-contained, comprehensive introduction to CAT(0) cube complexes Topics range from basic prerequisites to a variety of advanced topics Suitable for use in a graduate course or for independent study

Autor*in

Petra Schwer

Themen in »CAT(0) Cube Complexes«

CAT(0) Spaces Cube Complexes Geometric Group Theory Group Actions Polyhedral Complexes Gromov's Link Condition Hyperplanes Half-space Systems Cubulation Coxeter Groups Tits Alternative Helly Theorems Phylogenetic Trees

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“It is certainly a good resource for anyone seeking to teach such a course, or for self-study. Each chapter has a nice selection of about a dozen exercises. Necessarily the book does not cover several advanced topics, but it does give good motivation and pointers to further developments” (John M. Mackay, Mathematical Reviews, September 2, 2025)

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