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arXiv · 2606.19322

Existential Inclusions of Bi-exact Groups are Conjugacy Representation Rigid

Connor MacMahon
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Abstract

If $Λ$ is a non-amenable bi-exact group and $Λ\hookrightarrow Γ$ is an existential embedding, then each of the intersections $Λ\cap g Λg^{-1}$ for $g$ a member of $Γ\backslash Λ$ is amenable. This in conjunction with work of Bekka and Kalantar demonstrates that in this situation, the weak equivalence class of the quasi-regular representation $λ_{Γ/Λ}$ determines $Λ$ up to conjugacy among the self-commensurating subgroups of $Γ$.

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Connor MacMahon. 2026-06-17. Existential Inclusions of Bi-exact Groups are Conjugacy Representation Rigid. https://arxiv.org/abs/2606.19322

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