CAT(0) Cube Complexes: An Introduction (Lecture Notes in Mathematics, 2324) - Softcover

Schwer, Petra

Softcover

ISBN 10: 3031436210 ISBN 13: 9783031436215

Publisher: Springer, 2024

Synopsis

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.

About this title

About the Author

Petra Schwer is Professor of Mathematics at the Otto-von-Guericke University in Magdeburg, Germany. Prior to her current position she taught at Karlsruhe Institute of Technology (KIT) and Ruprecht-Karls-Universität Heidelberg. Petra Schwer studies the interplay between geometric objects and their symmetries. More specifically she works on topics in geometric group theory, metric geometry and combinatorial group theory and likes to apply these methods to adjacent areas. Her current focus is on non-positively curved groups and spaces, polyhedral complexes, as well as Coxeter groups, (Bruhat-Tits) buildings, and their applications.

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.

Edition details

• Publisher: Springer
• Publication date: 2024
• Language: English
• ISBN 10: 3031436210
• ISBN 13: 9783031436215
• Binding: Paperback
• Number of pages: 200