3 problems

Aschenbrenner–Friedl–Wilton's conjecture. If $H$ is a fully relatively quasiconvex subgroup of $\pi_1M$, then $H$ is a virtual retract. In particular, $H$ is separable.

Let $N$ be an orientable, compact, non-positively curved $3$-manifold with empty or toroidal boundary, and write $\pi=\pi_1(N)$. Equip $\pi$ with its natural relatively hyperbolic…

Let $N$ be a compact, orientable, irreducible $3$-manifold with empty or toroidal boundary. Suppose no torus of the JSJ decomposition bounds a Seifert fibered $3$-manifold on both…