Large scale geometry is the study of geometric objects viewed from a great distance. The idea of large scale geometry can be traced back to Mostow's work on rigidity and the work of Švarc, Milnor, and Wolf on growth of groups. In the last decades, large scale geometry has found important applications in group theory, topology, geometry, higher index theory, computer science, and large data analysis.

This book provides a friendly approach to the basic theory of this exciting and fast growing subject and offers a glimpse of its applications to topology, geometry, and higher index theory. The authors have made a conscientious effort to make the book accessible to advanced undergraduate students, graduate students, and non-experts.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

Readership

Advanced undergraduate students, graduate students, and non-experts interested in large scale geometry.

Table of Contents

• Metric spaces and large scale geometry
• Asymptotic dimension and decomposition complexity
• Amenability
• Property A
• Coarse embeddings
• Group actions on Banach spaces
• Coarse homology
• Survey of applications
• References
• Index