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

Abstract

This is part 2 of a 3-part article where we provide an $O(n^2)$-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.

Revision of part 2 with 9 pages, 13 figures of 3 part article

References in corpus (2)

• Framed link presentations of 3-manifolds by an $O(n^2)$ algorithm, I: gems and their duals
• Framed link presentations of 3-manifolds by an {O}(n^2) algorithm, III: geometric complex ${\mathcal{H}}_n^{\star }$ embedded into ${\mathbb{R}}^3$

Cited by in corpus (1)

• Framed link presentations of 3-manifolds by an $O(n^2)$ algorithm, I: gems and their duals