Nilpotent Cantor actions

Steven Hurder; Olga Lukina

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arXiv · 1905.07740

Nilpotent Cantor actions

Steven Hurder·Olga Lukina

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Abstract

A nilpotent Cantor action is a minimal equicontinuous action $\Phi \colon \Gamma \times \frak{X} \to \frak{X}$ on a Cantor set $\frak{X}$, where $\Gamma$ contains a finitely-generated nilpotent subgroup $\Gamma_0 \subset \Gamma$ of finite index. In this note, we show that these actions are distinguished among general Cantor actions: any effective action of a finitely generated group on a Cantor space, which is continuously orbit equivalent to a nilpotent Cantor action, must itself be a nilpotent Cantor action. As an application of this result, we obtain new invariants of nilpotent Cantor actions under continuous orbit equivalence.

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BibTeX RIS

Steven Hurder, Olga Lukina. 2019-05-19. Nilpotent Cantor actions. https://arxiv.org/abs/1905.07740

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