4 problems

Word-hyperbolicity conjecture. The mapping torus $G_\phi$ is word-hyperbolic if and only if it does not contain Baumslag–Solitar subgroups.

Kapovich–Weidmann higher-stabilization conjecture. For every $1\le t<m$, the generating $(k+t)$-tuple $(a_1,\ldots,a_k,1,\ldots,1)$ is not equivalent to a $(k+t)$-tuple of type…

Kapovich–Weidmann stabilization conjecture. In the above construction, at least $k$ stabilizations are needed to make the tuples $(a_1,\ldots,a_k)$ and $(b_1,\ldots,b_k)$ Nielsen e…

Let $F$ be a finitely generated free group and let $G$ be the mapping torus of an endomorphism of $F$. A Baumslag–Solitar subgroup means a subgroup isomorphic to a group of the for…