Geometric Group Theory
About this Title
Mladen Bestvina, University of Utah, Salt lake City, UT, Michah Sageev, Technion-Israel institute of Technology, Haifa, Israel and Karen Vogtmann, University of Warwick, Coventry, UK, Editors
Publication: IAS/Park City Mathematics Series
Publication Year: 2014; Volume 21
ISBNs: 978-1-4704-1227-2 (print); 978-1-4704-1998-1 (online)
MathSciNet review: MR3307635
MSC: Primary 20-06
Geometric group theory refers to the study of discrete groups using tools from topology, geometry, dynamics and analysis. The field is evolving very rapidly and the present volume provides an introduction to and overview of various topics which have played critical roles in this evolution.
The book contains lecture notes from courses given at the Park City Math Institute on Geometric Group Theory. The institute consists of a set of intensive short courses offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The courses begin at an introductory level suitable for graduate students and lead up to currently active topics of research. The articles in this volume include introductions to CAT(0) cube complexes and groups, to modern small cancellation theory, to isometry groups of general CAT(0) spaces, and a discussion of nilpotent genus in the context of mapping class groups and CAT(0) groups. One course surveys quasi-isometric rigidity, others contain an exploration of the geometry of Outer space, of actions of arithmetic groups, lectures on lattices and locally symmetric spaces, on marked length spectra and on expander graphs, Property tau and approximate groups.
This book is a valuable resource for graduate students and researchers interested in geometric group theory.
Graduate students and research mathematicians interested in geometric group theory.
Table of Contents
- CAT(0) cube complexes and groups
- Geometric small cancellation
- Lectures on proper CAT(0) spaces and their isometry groups
- Lectures on quasi-isometric rigidity
- Geometry of outer space
- Some arithmetic groups that do not act on the circle
- Lectures on lattices and locally symmetric spaces
- Lectures on marked length spectrum rigidity
- Expander graphs, property $(\tau )$ and approximate groups
- Cube complexes, subgroups of mapping class groups, and nilpotent genus