How to get a strongly aperodic SFT in the Grigorchuk group
Sebastián Barbieri  1@  
1 : ENS DE LYON
École Normale Supérieure - Lyon

(exposé au tableau)

An action of a finitely generated group over a Cantor set is called effectively closed if there is a Turing machine which recieves as input a cylinder and a generator and computes an effective aproximation of the complement of the image of such cylinder under the generator. I will show that every effectively closed action of a finitely generated group $G$ can be realized as a factor of the $G$-subaction of an SFT in $G \times H_1 \times H_2$ for any pair of infinite f.g. groups $H_1,H_2$. As a corollary we obtain that any group of the form $G_1 \times G_2 \times G_3$ admits a strongly aperiodic SFT whenever all the $G_i$ are finitely generated and have decidable word problem. In particular, we show how this theorem implies the existence of strongly aperiodic SFTs in the Grigorchuk group.


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