13 problems

A finitely generated group $G$ is co-context-free if its co-word problem is context-free. Thompson's group $V$ is the group of homeomorphisms represented by finite binary tree-pair…

Let a group $\Gamma$ act faithfully on a set $S$. The action is of type (A) if $\Gamma$ is finitely presented, every stabilizer $\operatorname{Stab}_{\Gamma}(s)$ is finitely genera…

A finitely generated group is co-context-free if its word problem's complement is context-free. The co-context-free embedding conjecture. A finitely generated group is co-context-f…

Hopficity conjecture. $V(G)$ is Hopfian if and only if $G$ is Hopfian.

Let $BF_n(\{1\})$ and $BF_n(\mathcal{P}_n)$ be the groups associated respectively with the trivial label group and with the pure braid group $\mathcal{P}_n$ in the construction of…

Let $d\geq 2$ and $r\geq 1$, let $B_d$ be the braid group with $d$ strings, and let $H\leq B_d$ be a finitely presented subgroup. The group $bV_{d,r}(H)$ is the labeled braided Hig…

Normalish subgroup conjecture. Every normalish subgroup of $T$ contains an embedded copy of R. Thompson's group $F$ or an embedded non-abelian free subgroup.

Let $V$ be R. Thompson's group, and call a group a $co\mathcal{CF}$ group if and only if it embeds as a finitely generated subgroup of $QAut(\mathscr{T}_{2,c})$. Lehnert's conjectu…

Universality conjecture for $V$. The classes $\mathcal{V}$ and $co\mathcal{CF}$ are equal:

Let $\Vloop=\Thomp{\mathit{LB}_*}$ and $\Floop=\Thomp{\mathit{PLB}_*}$ be the generalized Thompson groups containing the loop braid groups and pure loop braid groups, respectively.…

Let $\Vmock$ be the generalized Thompson group built from the family of mock symmetric groups. Finiteness conjecture. The group $\Vmock$ is of type $\mathrm{F}_\infty$. This is exp…

Finiteness equivalence conjecture.

Growth-rate conjecture. The growth rate is