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This is a Quantitative Study study.

October 3, 2025Open Access

Graphical small cancellation and hyperfiniteness of boundary actions

Key Points

The study shows that graphical small cancellation groups can have hyperfinite boundary actions, which impacts their dynamics.
Hyperfinite characteristics are established for the orbit equivalence relations on the Gromov boundaries of coned-off Cayley graphs.
A class of infinitely presented graphical small cancellation groups is included, enhancing the previous classical results.
The findings have implications for understanding the structural properties of actions on geometrically defined boundaries.

Abstract

We study actions of (infinitely presented) graphical small cancellation groups on the Gromov boundaries of their coned-off Cayley graphs. We show that a class of graphical small cancellation groups, including (infinitely presented) classical small cancellation groups, admit hyperfinite boundary actions, more precisely, the orbit equivalence relation that they induce on the boundaries of the coned-off Cayley graphs is hyperfinite.

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Cite This Study

Karpinski et al. (Sat,) studied this question.

synapsesocial.com/papers/68e034f7f0e39f13e7fa303e https://doi.org/https://doi.org/10.48550/arxiv.2509.05548

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