7 problems

Fibered homotopy K-theory isomorphism conjecture. The group $G$ satisfies the (fibered) $\mathit{KH}$-isomorphism conjecture for $R$ if the pair $(G,\mathcal{FIN})$ satisfies the (…

Let $T$ be a simplicial tree, and let $X=(g_1,\dots,g_n)$ be an $n$-tuple of isometries of $T$. A product replacement replaces some $g_i$ by either $g_jg_i$ or $g_ig_j^{-1}$ for…

Let $G$ be a finitely generated group acting on a tree, and consider both Weidmann's accessibility bound for $(k,C)$-acylindrical actions on a $C$-partially reduced tree and Bestvi…

Let $G$ be a finitely generated group acting on a tree, with the action subject to the hypotheses in Weidmann's accessibility theorem and with edge stabilisers restricted as in Bes…

Family-stabiliser tree conjecture. The inequality $\operatorname{cd}_{\mathcal{F}}G\leqslant 1$ holds if and only if $G$ acts on a tree whose stabilisers generate $\mathcal{F}$.

Type I conjecture. Under these assumptions, $G$ is a type I group.

Open amalgams conjecture. Every completely metrisable topological group has property (OA).