Lamplighters admit weakly aperiodic SFTs

  • David Bruce Cohen

    University of Chicago, USA
Lamplighters admit weakly aperiodic SFTs cover

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Let be a finite set and a group. A closed subset of is called a subshift if the action of on preserves . If is a closed subset of such that membership in is determined by looking at a fixed finite set of coordinates, and is the intersection of all translates of under the action of , then is called a subshift of finite type (SFT). If an SFT is nonempty and contains no finite -orbits, it is said to be weakly aperiodic. A virtually cyclic group has no weakly aperiodic SFT, and Carroll and Penland have conjectured that a group with no weakly aperiodic SFT must be virtually cyclic. Answering a question of Jeandel, we show that lamplighters always admit weakly aperiodic SFTs.

Cite this article

David Bruce Cohen, Lamplighters admit weakly aperiodic SFTs. Groups Geom. Dyn. 14 (2020), no. 4, pp. 1241–1252

DOI 10.4171/GGD/579