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Hyperfiniteness of boundary actions of cubulated hyperbolic groups
Published online by Cambridge University Press: 25 March 2019
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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