Verified Computations for Hyperbolic 3-Manifolds

DOI10.1080/10586458.2015.1029599zbMath1337.57044arXiv1310.3410OpenAlexW1926392198MaRDI QIDQ2801070

Kazuhiro Ichihara, Shin'ichi Oishi, Akitoshi Takayasu, Hidetoshi Masai, Neil R. Hoffman, Masahide Kashiwagi

Publication date: 19 April 2016

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.3410

zbMATH Keywords

hyperbolic 3-manifoldinterval arithmeticverified numerical computationsKrawczyk's test

Mathematics Subject Classification ID

General methods in interval analysis (65G40) General geometric structures on low-dimensional manifolds (57M50)

Related Items (21)

Absolutely exotic compact 4-manifolds ⋮ Knot concordances in $S^1\times S^2$ and exotic smooth $4$-manifolds ⋮ Cosmetic banding on knots and links ⋮ Practical bounds for a Dehn parental test ⋮ Norms on the cohomology of hyperbolic 3-manifolds ⋮ Equivariant hyperbolization of 3-manifolds via homology cobordisms ⋮ Infinitely many virtual geometric triangulations ⋮ Prime amphicheiral knots with free period 2 ⋮ On constraints for knots to admit chirally cosmetic surgeries and their calculations ⋮ On the geometry of rod packings in the 3‐torus ⋮ Floer homology, group orderability, and taut foliations of hyperbolic 3-manifolds ⋮ On satellite knots with symmetric union presentations ⋮ The Seiberg-Witten equations and the length spectrum of hyperbolic three-manifolds ⋮ Random veering triangulations are not geometric ⋮ Experimental Statistics of Veering Triangulations ⋮ A census of exceptional Dehn fillings ⋮ A Survey of the Impact of Thurston’s Work on Knot Theory ⋮ Ideal points of character varieties, algebraic non-integral representations, and undetected closed essential surfaces in 3–manifolds ⋮ hikmot ⋮ Verified computations for closed hyperbolic 3‐manifolds ⋮ Rigorous computations with an approximate Dirichlet domain

Uses Software

• Boost C++ Libraries
• SnapPy
• Snap

Cites Work

• Exceptional Dehn surgery on the minimally twisted five-chain link
• Proving a manifold to be hyperbolic once it has been approximated to be so
• Volumes of hyperbolic three-manifolds
• Homotopy hyperbolic 3-manifolds are hyperbolic
• Fehlerabschätzung reeller Eigenwerte und Eigenvektoren von Matrizen
• Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken
• Verification methods: Rigorous results using floating-point arithmetic
• Introduction to Automatic Differentiation and MATLAB Object-Oriented Programming
• Three dimensional manifolds, Kleinian groups and hyperbolic geometry
• A census of cusped hyperbolic 3-manifolds
• Computing Arithmetic Invariants of 3-Manifolds
• Symmetries, Isometries and Length Spectra of Closed Hyperbolic Three-Manifolds

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