Koichi Oyakawa

activity

20242026

collaborators

6 papers

math.GR2026

Graphical small cancellation and hyperfiniteness of boundary actions

Chris Karpinski, Damian Osajda, Koichi Oyakawa

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 ca…

math.GR2026

Hyperfiniteness of the boundary action of virtually special groups

Koichi Oyakawa

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 hyperfinit…

math.GR2025

Hyperfiniteness for group actions on trees

Srivatsav Kunnawalkam Elayavalli, Koichi Oyakawa, Forte Shinko +1

We identify natural conditions for a countable group acting on a countable tree which imply that the orbit equivalence relation of the induced action on the Gromov boundary is Bore…

math.GR2025

Small cancellation groups are bi-exact

Koichi Oyakawa

We prove that finitely generated (not necessarily finitely presented) $C^{'} (\frac{1}{33})$ -groups are bi-exact. This is a new class of bi-exact groups.

math.GR2024

Hyperfiniteness of boundary actions of acylindrically hyperbolic groups

Koichi Oyakawa

We prove that for any countable acylidrically hyperbolic group $G$ , there exists a generating set $S$ of $G$ such that the corresponding Cayley graph $I^ (G, S)$ is hyperbolic, $|\pa…

math.GR2024

Bi-exactness of relatively hyperbolic groups

Koichi Oyakawa

We prove that finitely generated relatively hyperbolic groups are bi-exact if and only if all peripheral subgroups are bi-exact. This is a generalization of Ozawa's result which cl…