Gespeichert in:
| 1. Verfasser: | |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2207.04980 |
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Inhaltsangabe:
- On this paper we will present a construction of a CAT(0) cube complex (an infinite cube), on which the uncountable family of Grigorchuk groups $G_ω$ act without bounded orbit. Moreover, if the sequence $ω$ does not contain repetition, we prove that the action is proper and faithful. As a consequence of this result, this cube complex is a model for the classifying space of proper actions for all the groups $G_ω$ with $ω$ without repetition. This construction works in a general way for any group acting on a set and which admits a commensurated subset.These examples of non-elliptic actions of infinite finitely generated torsion groups on a non-positively curved cube complex contrast to several established fixed-point theorems concerning actions of torsion groups.