3 problems

Waldhausen–Thurston conjecture. $M$ has a finite cover which is Haken.

A knot manifold is an irreducible, orientable, compact 3-manifold whose boundary is a single torus. It is hyperbolic if its interior admits a complete hyperbolic metric of finite v…

Let $N$ be a closed hyperbolic 3-manifold. A finite-sheeted Haken covering of $N$ is a finite-sheeted covering space of $N$ that is Haken. Effective virtual Haken conjecture. Every…