Large scale geometry of automorphism groups

TL;DR

This paper explores the large scale geometric properties of automorphism groups of countable structures, focusing on non-Archimedean Polish groups, and extends previous work on metrisable groups.

Contribution

It provides a detailed analysis of the large scale geometry of automorphism groups of countable structures, a specific case within the broader study of metrisable groups.

Findings

Characterization of large scale geometric properties of automorphism groups

Extension of large scale geometry theory to non-Archimedean Polish groups

Connections between group actions and geometric structures

Abstract

The present article constitutes the third part of our study of the large scale geometry of metrisable groups, the first two part appearing in the companion paper "Large scale geometry of metrisable groups". In this third part, we present a detailed study of the theory in the special case of non-Archimedean Polish groups, that is, automorphism groups of countable first order structures.