The visibility-end conjecture for finite-volume nonpositive-curvature manifolds

Let $M$ be a complete noncompact Riemannian manifold of finite volume with sectional curvature $-1\leq K\leq 0$. Suppose that the universal cover of $M$ is a visibility manifold, meaning that any two distinct points on its geometric boundary can be joined by a geodesic line. An end of $M$ has an almost nilpotent fundamental group if that group contains a nilpotent subgroup of finite index.

Visibility-end conjecture. The fundamental group of each end of $M$ is almost nilpotent.

This folklore conjecture concerns the algebraic structure of end groups in finite-volume nonpositive-curvature manifolds. The source states that it had been open for decades, while the accompanying theorem proves it in all dimensions; thus the conjecture is solved.