Zooming in on the large-scale geometry of locally compact groups

TL;DR

This survey explores how locally compact groups can be analyzed through geometric perspectives, highlighting key ideas and concepts without detailed proofs, serving as an accessible overview of the field.

Contribution

It provides a comprehensive overview of the geometric approach to locally compact groups, summarizing main ideas and concepts in the area.

Findings

Locally compact groups can be effectively studied as geometric objects.

The survey emphasizes core ideas and frameworks in the geometric analysis of these groups.

References to detailed proofs and further reading are provided for in-depth study.

Abstract

The purpose of this survey is to describe how locally compact groups can be studied as geometric objects. We will emphasize the main ideas and skip or just sketch most proofs, often referring the reader to our much more detailed book arXiv:1403.3796