3 problems

Uniform convergence conjecture. This action is a uniform convergence group.

Mapping torus convergence-group conjecture. For any p-A-like element $\phi$ of $G$, the mapping torus subgroup $G_\phi$ acts on $S^2$ as a convergence group.

Promotion of pseudo-fibering conjecture. There are three possibilities: $G$ is elementary; $G$ is a Fuchsian group; or $G$ is a closed hyperbolic $3$-manifold group.