Framed link presentations of 3-manifolds by an O(n2) algorithm, II: colored complexes and boundings in their complexity

Given an special type of triangulation T for an oriented closed 3-manifold M3 we produce a framed link in S3 which induces the same M3 by an algorithm of complexity O(n2) where n is the number of tetrahedra in T. The special class is formed by the duals of the solvable gems. These are in practice computationaly easy to obtain from any triangulation for M3. The conjecture that each closed oriented 3-manifold is induced by a solvable gem has been verified in an exhaustible way for manifolds induced by gems with few vertices. Our algorithm produces framed link presentations for well known 3-manifolds which hitherto did not one explicitly known. A consequence of this work is that the 3-manifold invariants which are presently only computed from surgery presentations (like the Witten-Reshetkhin-Turaev invariant) become computable also from triangulations. This seems to be a new and useful result. Our exposition is partitioned into 3 articles. This first article provides our motivation, some history on presentation of 3-manifolds and recall facts about gems which we need.