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

研究成果: Article › 査読

20 被引用数 (Scopus)

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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.

本文言語	English
ページ（範囲）	66-78
ページ数	13
ジャーナル	Experimental Mathematics
巻	25
号	1
DOI	https://doi.org/10.1080/10586458.2015.1029599
出版ステータス	Published - 2016 1月 2
外部発表	はい

ASJC Scopus subject areas

数学 (全般)

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10.1080/10586458.2015.1029599

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AU - Oishi, Shinichi

AU - Takayasu, Akitoshi

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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.

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KW - verified numerical computations

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Verified Computations for Hyperbolic 3-Manifolds

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