Graphical small cancellation and hyperfiniteness of boundary actions

2025/09/06 by Karpinski, Chris, Osajda, Damian, Oyakawa, Koichi
#03E15 #20F65 #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO)

paper · doi:10.48550/arxiv.2509.05548

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.

Citations

• Hyperfiniteness of boundary actions of acylindrically hyperbolic groups
• Hyperfiniteness and Borel asymptotic dimension of boundary actions of hyperbolic groups
• Hyperfiniteness of boundary actions of relatively hyperbolic groups
• Infinitely presented graphical small cancellation groups are\n acylindrically hyperbolic
• Small cancellation labellings of some infinite graphs and applications

Cited by

• Hyperfiniteness of the boundary action of virtually special groups

Related

• Actions of small cancellation groups on hyperbolic spaces
• Hyperfiniteness of boundary actions of acylindrically hyperbolic groups
• Small cancellation labellings of some infinite graphs and applications
• Hyperfiniteness of boundary actions of relatively hyperbolic groups
• Relative Hyperbolicity of Graphical Small Cancellation Groups