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arXiv · 1701.03969

Hyperfiniteness of boundary actions of cubulated hyperbolic groups

Jingyin Huang·Marcin Sabok·Forte Shinko
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Abstract

We show that if a hyperbolic group acts geometrically on a CAT(0) cube complex, then the induced boundary action is hyperfinite. This means that for a cubulated hyperbolic group the natural action on its Gromov boundary is hyperfinite, which generalizes an old result of Dougherty, Jackson and Kechris for the free group case.

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Jingyin Huang, Marcin Sabok, Forte Shinko. 2017-01-14. Hyperfiniteness of boundary actions of cubulated hyperbolic groups. https://doi.org/10.1017/etds.2019.5

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