The domino problem is undecidable on surface groups

Nathalie Aubrun, Sebastián Barbieri, Etienne Moutot

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.

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