11 problems

Let $G$ be the fundamental group of a non-positively curved graph manifold, let $X$ be its universal cover, and let $T_{\infty}$ be the Bass–Serre tree of the graph-of-groups decom…

Let $G$ act geometrically on two $\operatorname{CAT}(0)$ spaces $Y$ and $Y'$ whose $d_L$-metrics stabilize. Let $\partial_M^{\kappa}Y$ and $\partial_M^{\kappa}Y'$ denote their…

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 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…

Connectivity conjecture. A Coxeter group has connected, non-empty Morse boundary if and only if it is one-ended and wide-avoidant.

Fix, for every integer $n\geq 1$, the fundamental group $G_n$ of an $(n+2)$-dimensional cusped hyperbolic manifold. Let $\bar n$ be a finite collection of integers at least $1$, an…

Connectivity conjecture. For every $\epsilon>0$, if

Let $\Lambda$ be a graph, and let … be its associated right-angled Coxeter group. A finitely generated group has a quasi-isometry invariant Morse boundary, denoted…

Let $X$ and $Y$ be proper, cocompact CAT(0) spaces, and let $f:\partial_*X\to\partial_*Y$ be a homeomorphism, where $\partial_*X$ and $\partial_*Y$ denote their Morse boundaries. A…

Let $\Gamma$ be the defining graph of a right-angled Coxeter group $G_\Gamma$. An induced loop $\sigma$ in $\Gamma$ has length greater than $4$ and its vertex set contains no pair…

Let $n$-vertex graphs be sampled from a random graph model with density greater than $1/n$ and bounded away from $1$, and let the associated right-angled Coxeter group be the group…