The domino problem is undecidable on surface groups

Nathalie Aubrun, Sebastián Barbieri, Etienne Moutot

Published 2018-11-20Version 1

We show that the domino problem is undecidable on orbit graphs of non-deterministic substitutions which satisfy a technical property. As an application, we prove that the domino problem is undecidable for the fundamental group of any closed orientable surface of genus at least 2.