Coarse Bundles

TL;DR

This paper introduces a coarse geometric framework for understanding group extensions and actions on metric spaces, providing a complete classification for groups acting on trees with Abelian stabilizers.

Contribution

It develops a new coarse notion of bundle and applies it to classify groups acting on trees with Abelian stabilizers.

Findings

Complete classification of groups acting on trees with Abelian stabilizers

New coarse geometric tools for analyzing group actions

Insights into the structure of group extensions in coarse geometry

Abstract

We develop a coarse notion of bundle and use it to understand the coarse geometry of group extensions and, more generally, groups acting on proper metric spaces. The results are particularly sharp for groups acting on (locally finite) trees with Abelian stabilizers, which we are able to classify completely.