Hyperbolization Conjecture for closed irreducible 3-manifolds

Let $M$ be a closed, connected, ${\mathbf{P}^2}$-irreducible $3$-manifold with infinite fundamental group. Hyperbolization Conjecture. If $\pi_1(M)$ contains no subgroup isomorphic to $\mathbf{Z}\oplus\mathbf{Z}$, then $M$ is hyperbolic. This is one of the conjectures attributed in the source to Thurston and is presented as equivalent, together with the virtual bundle conjecture, to the hyperbolic case of geometrization; the source gives no resolution.