The triangulation complexity of elliptic and sol 3-manifolds
Marc Lackenby, Jessica S. Purcell
TL;DR
This paper computes the minimal number of tetrahedra needed to triangulate all elliptic and sol 3-manifolds, providing a comprehensive understanding of their triangulation complexities within a bounded error.
Contribution
It provides the first complete calculation of triangulation complexity for all elliptic and sol 3-manifolds, within a universal multiplicative error.
Findings
Triangulation complexity of elliptic 3-manifolds is determined.
Triangulation complexity of sol 3-manifolds is determined.
Complexity calculations are accurate within a bounded multiplicative factor.
Abstract
The triangulation complexity of a compact 3-manifold is the minimal number of tetrahedra in any triangulation of the 3-manifold. We compute the triangulation complexity of all elliptic 3-manifolds and all sol 3-manifolds, to within a universally bounded multiplicative error.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Advanced Graph Theory Research · Complexity and Algorithms in Graphs