# Strongly aperiodic subshifts of finite type on hyperbolic groups

## TL;DR

This paper establishes a precise condition under which hyperbolic groups can support strongly aperiodic subshifts of finite type, linking the property to the group's number of ends.

## Contribution

It provides a complete characterization of hyperbolic groups that admit strongly aperiodic subshifts of finite type based on their ends.

## Key findings

- Hyperbolic groups with at most one end admit strongly aperiodic subshifts of finite type.
- Hyperbolic groups with more than one end do not admit such subshifts.
- The result connects geometric group theory with symbolic dynamics.

## Abstract

We prove that a hyperbolic group admits a strongly aperiodic subshift of finite type if and only if it has at most one end.