Abstract:If $\Lambda$ is a non-amenable bi-exact group and $\Lambda \hookrightarrow \Gamma$ is an existential embedding, then each of the intersections $\Lambda \cap g \Lambda g^{-1}$ for $g$ a member of $\Gamma \backslash \Lambda$ 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 $\lambda_{\Gamma/\Lambda}$ determines $\Lambda$ up to conjugacy among the self-commensurating subgroups of $\Gamma$.
From: Connor MacMahon [view email]
[v1]
Wed, 17 Jun 2026 17:49:15 UTC (7 KB)
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