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Hyperfiniteness of boundary actions of cubulated hyperbolic groups. (English) Zbl 07228223
Summary: 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.
03E15 Descriptive set theory
20F65 Geometric group theory
Full Text: DOI
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