Framed link presentations of 3-manifolds by an $ O (n^ 2) $ algorithm, II: colored complexes and boundings in their complexity

摘要: This is part 2 of a 3-part article where we provide an -algorithm to produce a surgery presentation of a 3-manifold induced by a gem with a resolution. In this part we produce a sequence of colored simplicial 2-complexes which are inverses and dual to the sequence of gems produced in the first part. The refinements of the DPL-faces that keep appearing are idempotent: the second refinement of a DPL-face is isomorphic to its first refinement. This fact inhibits exponentiability.