Hyperfiniteness of boundary actions of cubulated hyperbolic groups

Published 14 Jan 2017 in math.GR and math.LO | (1701.03969v2)

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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