Hyperfiniteness of boundary actions of cubulated hyperbolic groups

Hyperfiniteness of boundary actions of cubulated hyperbolic groups

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 Kechr...

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Veröffentlicht in:Ergodic theory and dynamical systems 2020-09, Vol.40 (9), p.2453-2466
Hauptverfasser: HUANG, JINGYIN, SABOK, MARCIN, SHINKO, FORTE
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2019.5