Geometrizable three-manifold
= Geometrizable three-manifold
A closed orientable <three-manifold> is geometrizable if its prime summands can be split along finitely many disjoint essential <tori> into pieces whose interiors carry complete geometric structures modeled on the eight <Thurston geometries>. Prime decomposition and capping sphere boundaries precede the torus cuts; a single homogeneous geometry on the original connected sum is not required.