150 research outputs found
Translation-like Actions and Aperiodic Subshifts on Groups
It is well known that if admits a f.g. subgroup with a weaklyaperiodic SFT (resp. an undecidable domino problem), then itself has a weakly aperiodic SFT (resp. an undecidable domino problem).We prove that we can replace the property " is a subgroup of "by " acts translation-like on ", provided is finitely presented.In particular:* If and are f.g. infinite groups, then has a weakly aperiodic SFT (and actually a undecidable domino problem). In particular the Grigorchuk group has an undecidable domino problem. * Every infinite f.g. -group admits a weakly aperiodic SFT
On the noncommutative geometry of tilings
This is a chapter in an incoming book on aperiodic order. We review results
about the topology, the dynamics, and the combinatorics of aperiodically
ordered tilings obtained with the tools of noncommutative geometry
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