CK-admissible groups' Cantor-chain conjecture for visual sublinearly Morse boundaries

Let $G$ be a CK-admissible group acting geometrically on a Hadamard space $Y$. Let $T_{\infty}$ be the Bass–Serre tree associated to the graph-of-groups structure of $G$, and let $\partial_{\kappa}Y$ denote the $\kappa$-Morse boundary. The topology $\mathcal{T}(G,[T_{\infty}])$ is induced by the action on $T_{\infty}$. CK-admissible Cantor-chain conjecture. The space $(\partial_{\kappa}Y,\mathcal{T}(G,[T_{\infty}]))$ is a Cantor chain and coincides with $\partial_{\kappa}Y$ equipped with the visual topology. This conjecture extends the graph-manifold result to CK-admissible groups, whose Bass–Serre actions are largest acylindrical actions; the general statement remains open.