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October 3, 2025Open Access

Hyperfiniteness of the boundary action of virtually special groups

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The boundary action of virtually special groups exhibits hyperfiniteness, impacting its orbit equivalence relation.
This work generalizes the previously established hyperfiniteness in cubulated hyperbolic groups' boundary actions.
Orbit equivalence relations linked to CAT(0) cube complexes demonstrate significant behavior patterns in group theory.
Understanding these properties enhances the comprehension of group actions and their implications in geometry.

Implication

Proving hyperfiniteness of orbit equivalence relations in CAT(0) cube complexes for virtually special groups, indicating broader implications.

Abstract

We prove that for any countable group acting virtually specially on a CAT(0) cube complex, the orbit equivalence relation induced by its action on the Roller boundary is hyperfinite. This can be considered as a generalization of hyperfiniteness of the boundary action of cubulated hyperbolic groups by Huang-Sabok-Shinko.

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Cite This Study

Koichi Oyakawa (2025) studied this question.

synapsesocial.com/papers/68e02f40f0e39f13e7fa2aa3 https://doi.org/10.48550/arxiv.2509.04613

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Implication

Proving hyperfiniteness of orbit equivalence relations in CAT(0) cube complexes for virtually special groups, indicating broader implications.

Hyperfiniteness of the boundary action of virtually special groups

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Implication

Abstract

Discussion

Cite This Study

Hyperfiniteness of the boundary action of virtually special groups

Key Points

Implication

Abstract

Discussion

Cite This Study

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