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

2012/11/09 by Sóstenes Lins, Ricardo Machado, Lins, Sóstenes +1
Computer Science · Mathematics · #57M15 (Secondary) #57M25 #57Q15 (Primary) 57M27 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1212.0826

openalex publication_date 2012/11/09 · openalex created_date 2016/08/23 · openalex updated_date 2026/07/28

Abstract

This is part 2 of a 3-part article where we provide an O(n²)-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.

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• Framed link presentations of 3-manifolds by an O(n²) algorithm, I:\n gems and their duals

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