Thurston's geometric decomposition conjecture for compact prime 3-manifolds

Let $M$ be a compact, orientable, prime $3$-manifold. The eight Thurston geometries are the homogeneous geometries that admit compact quotient manifolds. Thurston's geometric decomposition conjecture. There is a finite collection of disjoint, embedded, incompressible tori in $M$ such that each component of the complement admits a geometric structure modeled on one of the eight Thurston geometries. This is the geometric decomposition aspect of Thurston's geometrization theorem and was established as part of the proof of geometrization.