# Polish Topologies for Graph Products of Cyclic Groups

## TL;DR

This paper characterizes which graph products of cyclic groups can have a Polish group topology, showing they can be realized as automorphism groups of countable structures, and applies this to right-angled Coxeter and Artin groups.

## Contribution

It provides a complete characterization of graph products of cyclic groups with Polish topologies, extending previous results to broader classes of groups.

## Key findings

- Characterization of graph products of cyclic groups with Polish topology
- Realization of these groups as automorphism groups of countable structures
- Application to right-angled Coxeter and Artin groups

## Abstract

We give a complete characterization of the graph products of cyclic groups admitting a Polish group topology, and show that they are all realizable as the group of automorphisms of a countable structure. In particular, we characterize the right-angled Coxeter groups (resp. Artin groups) admitting a Polish group topology. This generalizes results from [5], [7] and [4].