A geometric simulation theorem on direct products of finitely generated groups
Discrete analysis (2019)
Voir la notice de l'article provenant de la source Scholastica
arXiv
We show that every effectively closed action of a finitely generated group $G$ on a closed subset of $\{0,1\}^{\mathbb{N}}$ can be obtained as a topological factor of the $G$-subaction of a $(G \times H_1 \times H_2)$-subshift of finite type (SFT) for any choice of infinite and finitely generated groups $H_1,H_2$. As a consequence, we obtain that every group of the form $G_1 \times G_2 \times G_3$ admits a non-empty strongly aperiodic SFT subject to the condition that each $G_i$ is finitely generated and has decidable word problem. As a corollary of this last result we prove the existence of non-empty strongly aperiodic SFT in a large class of branch groups, notably including the Grigorchuk group.
Sebastián Barbieri. A geometric simulation theorem on direct products of finitely generated groups. Discrete analysis (2019). http://geodesic.mathdoc.fr/item/DAS_2019_a11/
@article{DAS_2019_a11,
author = {Sebasti\'an Barbieri},
title = {A geometric simulation theorem on direct products of finitely generated groups},
journal = {Discrete analysis},
year = {2019},
language = {en},
url = {http://geodesic.mathdoc.fr/item/DAS_2019_a11/}
}