Geometric Group Theory: An Introduction (Universitext) - Softcover

Löh, Clara

Softcover

ISBN 10: 3319722530 ISBN 13: 9783319722535

Publisher: Springer, 2018

Synopsis

Inspired by classical geometry, geometric group theory has in turn provided a variety of applications to geometry, topology, group theory, number theory and graph theory. This carefully written textbook provides a rigorous introduction to this rapidly evolving field whose methods have proven to be powerful tools in neighbouring fields such as geometric topology.

Geometric group theory is the study of finitely generated groups via the geometry of their associated Cayley graphs. It turns out that the essence of the geometry of such groups is captured in the key notion of quasi-isometry, a large-scale version of isometry whose invariants include growth types, curvature conditions, boundary constructions, and amenability.

This book covers the foundations of quasi-geometry of groups at an advanced undergraduate level. The subject is illustrated by many elementary examples, outlooks on applications, as well as an extensive collection of exercises.

About this title

About the Author

Clara Löh is Professor of Mathematics at the University of Regensburg, Germany. Her research focuses on the interaction between geometric topology, geometric group theory, and measurable group theory. This includes cohomological, geometric, and combinatorial methods. 

From the Back Cover

Inspired by classical geometry, geometric group theory has in turn provided a variety of applications to geometry, topology, group theory, number theory and graph theory. This carefully written textbook provides a rigorous introduction to this rapidly evolving field whose methods have proven to be powerful tools in neighbouring fields such as geometric topology.

Geometric group theory is the study of finitely generated groups via the geometry of their associated Cayley graphs. It turns out that the essence of the geometry of such groups is captured in the key notion of quasi-isometry, a large-scale version of isometry whose invariants include growth types, curvature conditions, boundary constructions, and amenability.

This book covers the foundations of quasi-geometry of groups at an advanced undergraduate level. The subject is illustrated by many elementary examples, outlooks on applications, as well as an extensive collection of exercises.

Edition details

• Publisher: Springer
• Publication date: 2018
• Language: English
• ISBN 10: 3319722530
• ISBN 13: 9783319722535
• Binding: Paperback
• Edition number: 1
• Number of pages: 400