3 problems

The Bieri–Stallings connectivity-at-infinity conjecture. For $n\geq 2$, the group $B_n$ is $(n-2)$-connected at infinity.

Let $k\geq 2$, let $\Gamma_1,\dots,\Gamma_n$ be groups of type $\operatorname{FP}_k$, and let $P\leq\Gamma_1\times\dots\times\Gamma_n$ be a subgroup of their direct product. Say th…

Let $\Gamma$ be a graph, let $A_\Gamma$ be its right-angled Artin group, and let $(w,Q)$ be a symplectic structure on $A_\Gamma$. Write $\mathrm{Mod}(\Gamma,w,Q)$ for the subgroup…