2024/02/22 by Laurent Bartholdi, Ville Salo, Bartholdi, Laurent +1
Engineering · #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Group Theory (math.GR) #Logic in Computer Science (cs.LO) #Physics and Engineering Research Articles
paper · pdf · doi:10.48550/arxiv.2402.14508
openalex publication_date 2024/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that the lamplighter group admits strongly aperiodic SFTs, has undecidable tiling problem, and the entropies of its SFTs are exactly the upper semicomputable nonnegative real numbers, and some other results. These results follow from two relatively general simulation theorems, which show that for a large class of effective subshifts on the sea-level subgroup, their induction to the lamplighter group is sofic; and the pullback of every effective Cantor system on the integers admits an SFT cover. We exhibit a concrete strongly aperiodic set with 1488 tetrahedra. We show that metabelian Baumslag-Solitar groups are intersimulable with lamplighter groups, and thus we obtain the same characterization for their entropies.