Three-manifold hierarchy
= Three-manifold hierarchy
A hierarchy is a finite sequence of cuts along properly embedded two-sided <incompressible surfaces>, without spherical components, ending in disjoint three-balls. <Disks> are allowed. For an ambient manifold which is not <orientable> the two-sided cutting <surfaces> need not themselves be <orientable>. The existence of a hierarchy does not imply that every choice of incompressible cuts terminates.