Strongly aperiodic subshifts of finite type on hyperbolic groups

David B Cohen,Yo’Av Rieck,Chaim Goodman-Strauss

doi:10.1017/etds.2021.70

Abstract

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

Highlights

This paper is devoted to proving the following theorem.THEOREM
We prove that a hyperbolic group admits a strongly aperiodic subshift of finite type if and only if it has at most one end
A hyperbolic group admits a strongly aperiodic subshift of finite type (SFT) if and only if it has at most one end

Summary

Introduction

This paper is devoted to proving the following theorem.THEOREM. A hyperbolic group admits a strongly aperiodic subshift of finite type (SFT) if and only if it has at most one end.Many groups are known to admit strongly aperiodic SFTs. We prove that a hyperbolic group admits a strongly aperiodic subshift of finite type if and only if it has at most one end. A hyperbolic group admits a strongly aperiodic subshift of finite type (SFT) if and only if it has at most one end.

Results

Conclusion