Verified Computations for Hyperbolic 3-Manifolds

Neil Hoffman; Kazuhiro Ichihara; Masahide Kashiwagi; Hidetoshi Masai; Shinichi Oishi; Akitoshi Takayasu

doi:10.1080/10586458.2015.1029599

Verified Computations for Hyperbolic 3-Manifolds

Neil Hoffman, Kazuhiro Ichihara, Masahide Kashiwagi, Hidetoshi Masai, Shinichi Oishi, Akitoshi Takayasu

Research output: Contribution to journal › Article › peer-review

27 Scopus citations

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 is an implementation of interval arithmetic and Krawczyks 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.

Original language	English (US)
Pages (from-to)	66-78
Number of pages	13
Journal	Experimental Mathematics
Volume	25
Issue number	1
DOIs	https://doi.org/10.1080/10586458.2015.1029599
State	Published - Jan 2 2016
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2015 Taylor and Francis Group, LLC.

Keywords

Krawczyk's test
hyperbolic 3-manifold
interval arithmetic
verified numerical computations

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10.1080/10586458.2015.1029599

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AU - Ichihara, Kazuhiro

AU - Kashiwagi, Masahide

AU - Masai, Hidetoshi

AU - Oishi, Shinichi

AU - Takayasu, Akitoshi

PY - 2016/1/2

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N2 - 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 is an implementation of interval arithmetic and Krawczyks 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.

AB - 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 is an implementation of interval arithmetic and Krawczyks 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.

KW - Krawczyk's test

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KW - interval arithmetic

KW - verified numerical computations

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Verified Computations for Hyperbolic 3-Manifolds

Abstract

Bibliographical note

Keywords

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