Simplifying triangulations of S^3
Aleksandar Mijatovic
TL;DR
This paper presents a method to simplify any triangulation of the 3-sphere using Pachner moves, providing explicit bounds and a new recognition algorithm for the 3-sphere.
Contribution
It introduces an explicit exponential bound on Pachner moves needed for simplification and develops a novel recognition algorithm for the 3-sphere.
Findings
Explicit exponential bound on Pachner moves for S^3 triangulations
A new algorithm for recognizing the 3-sphere
Improved understanding of triangulation simplification processes
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsComputational Geometry and Mesh Generation · Advanced Combinatorial Mathematics · Geometric and Algebraic Topology