Verified computations for hyperbolic 3-manifolds

2013/10/12 by Neil Hoffman, Hoffman, Neil, Kazuhiro Ichihara +9 · 3 citations
Computer Science · Mathematics · #57M50 #65G40 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1310.3410

openalex publication_date 2013/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a given cusped 3-manifold M admitting an ideal triangulation, we describe a method to rigorously prove that either M or a filling of M admits a complete hyperbolic structure via verified computer calculations. Central to our method are an implementation of interval arithmetic and Krawczyk's Test. These techniques represent an improvement over existing algorithms as they are faster, while accounting for error accumulation in a more direct and user friendly way.

Citations

• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds

Cited by

• FAMED by computer: proving the Andersen-Kashaev volume conjecture for 42,000 knots
• Tiling Hyperbolic Manifolds: Algorithms and Applications
• The complete 10-tetrahedra census of orientable cusped hyperbolic 3-manifolds

Related

• Computing complete hyperbolic structures on cusped 3-manifolds
• Tiling Hyperbolic Manifolds: Algorithms and Applications
• Construction and Recognition of Hyperbolic 3-Manifolds with Geodesic Boundary
• The complete 10-tetrahedra census of orientable cusped hyperbolic 3-manifolds
• The cusped hyperbolic census is complete