Geodesic
A geometric simulation theorem on direct products of finitely generated groups
Discrete analysis (2019) Cet article a éte moissonné depuis la source Scholastica

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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.
Publié le : 
@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/}
}
TY  - JOUR
AU  - Sebastián Barbieri
TI  - A geometric simulation theorem on direct products of finitely generated groups
JO  - Discrete analysis
PY  - 2019
UR  - http://geodesic.mathdoc.fr/item/DAS_2019_a11/
LA  - en
ID  - DAS_2019_a11
ER  - 
%0 Journal Article
%A Sebastián Barbieri
%T A geometric simulation theorem on direct products of finitely generated groups
%J Discrete analysis
%D 2019
%U http://geodesic.mathdoc.fr/item/DAS_2019_a11/
%G en
%F DAS_2019_a11
Sebastián Barbieri. A geometric simulation theorem on direct products of finitely generated groups. Discrete analysis (2019). http://geodesic.mathdoc.fr/item/DAS_2019_a11/