4 problems

Let $G$ be a hierarchically hyperbolic group (HHG), and let $\partial_M G$ be its Morse boundary. Assume that $G$ admits a largest acylindrical action. The topology on…

Let $G$ be a hierarchically hyperbolic group (HHG), and let $H<G$ be an infinite hyperbolic normal subgroup of infinite index. A Cannon–Thurston map is a continuous extension of th…

Cannon–Thurston map nonexistence conjecture. Such a map does not exist unless either $G$ is hyperbolic or $H$ is hierarchically quasiconvex in some HHG structure on $G$.

Let $S$ be any surface of finite type, and let $g_1,\dots,g_l\in \mathcal{MCG}^\pm(S)$. For a subgroup $H$ of a group $G$, write $\langle\langle H\rangle\rangle$ for its normal clo…