Simplifying triangulations of S³

2000/08/15 by Aleksandar Mijatović, Aleksandar Mijatovic, Mijatovic, Aleksandar
Computer Science · Mathematics · #57N12 #57Q15 #Advanced Combinatorial Mathematics #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.GT #msc:57N12 #msc:57Q15

paper · pdf · doi:10.48550/arxiv.math/0008107

27 pages, 18 figures

arxiv created 2000/08/15 · openalex publication_date 2000/08/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we describe a procedure to simplify any given triangulation of the 3-sphere using Pachner moves. We obtain an explicit exponential-type bound on the number of Pachner moves needed for this process. This leads to a new recognition algorithm for the 3-sphere.

Related

• Simplification paths in the Pachner graphs of closed orientable 3-manifold triangulations
• An upper bound on Pachner moves relating geometric triangulations
• Centrally symmetric and balanced triangulations of \mathbbS²× \mathbbS^d-3 with few vertices
• Triangulations of Seifert Fibred Manifolds
• Connecting 3-manifold triangulations with unimodal sequences of elementary moves