7 problems

Let $F_k$ be a free group of rank $k\ge 2$, let $\phi$ be an injective endomorphism of $F_k$, and let $\operatorname{HNN}_{\phi}(F_k)$ denote the corresponding ascending HNN extens…

Let $H$ be a hyperbolic group, and let $G$ be an ascending HNN-extension with base group $H$. Sapir–Wise conjecture. Every ascending HNN-extension with a hyperbolic base group is H…

Let $G'$ be a finitely generated free-by-cyclic group, and let $cvarphi\to\Phi$ denote an extension as in the diagram above, where the underlying free groups are finitely generated…

Bieri's conjecture. If

Let $F_k$ be a finite-rank free group and let $\theta:F_k\rightarrow F_k$ be an injective, non-surjective endomorphism. The associated strictly ascending HNN extension is…

Magnus–Moldavanskii tower conjecture. Every one-relator group of arbitrary depth is computably embeddable into a Magnus–Moldavanskii tower of HNN-extensions with the standard norma…

Let $C=F*_{\phi}$, where $F=\langle a,b\rangle$ is free and $\phi$ is the endomorphism given by … A Sapir's conjecture. The group $C$ does not contain a surface subgroup. This conj…