7 problems

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

Bi-${\rm FP}_\infty$ conjecture. Every one-relator monoid of the form $\langle A\mid u=v\rangle$ is of type bi-${\rm FP}_\infty$.

Let $A \to G \to Q$ be a short exact sequence of groups, with $G$ finitely generated and $A$ and $Q$ abelian. Regard $A$ as a right $\mathbb{Z}Q$-module via conjugation. Writing…

The $FP_m$-conjecture for metabelian groups. $\Gamma$ is of type $FP_n$ if and only if every $n$-point subset of $\Sigma^{0}(G;A)^c$ lies in an open hemisphere of…

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 $\mathbf{C}$ be a category. Say that $\mathbf{C}$ is bi-$\operatorname{FP}_n$ when the $\mathbf{C}^{\operatorname{op}}\times\mathbf{C}$-module $\mathbb{Z}\mathbf{C}$ is of type…

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…