Strongly aperiodic subshifts on surface groups

TL;DR

This paper constructs strongly aperiodic subshifts of finite type on hyperbolic surface groups and orbit graphs derived from primitive symbolic substitution systems with incommensurate growth rates, expanding the understanding of aperiodic tilings.

Contribution

It introduces a method to create strongly aperiodic subshifts on hyperbolic groups and orbit graphs from symbolic systems with incompatible growth rates.

Findings

Existence of strongly aperiodic subshifts on hyperbolic surface groups

Construction of aperiodic subshifts on orbit graphs from symbolic systems

Extension of aperiodic tiling theory to new classes of groups and graphs

Abstract

We give strongly aperiodic subshifts of finite type on every hyperbolic surface group; more generally, for each pair of expansive primitive symbolic substitution systems with incommensurate growth rates, we construct strongly aperiodic subshifts of finite type on their orbit graphs.