Hyperfiniteness of boundary actions of cubulated hyperbolic groups

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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References in corpus (3)

• Cubulating hyperbolic free-by-cyclic groups: the general case
• Measure reducibility of countable Borel equivalence relations
• On geodesic ray bundles in hyperbolic groups

Cited by in corpus (5)

• Hyperfiniteness of boundary actions of hyperbolic groups
• Unicorn paths and hyperfiniteness for the mapping class group
• Tree-like graphings, wallings, and median graphings of equivalence relations
• Graphical small cancellation and hyperfiniteness of boundary actions
• Hyperfiniteness for group actions on trees