Verified Computations for Hyperbolic 3-Manifolds

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

    Research output: Contribution to journalArticle

    10 Citations (Scopus)

    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 languageEnglish
    Pages (from-to)66-78
    Number of pages13
    JournalExperimental Mathematics
    Volume25
    Issue number1
    DOIs
    Publication statusPublished - 2016 Jan 2

    Fingerprint

    Hyperbolic 3-manifold
    Hyperbolic Structure
    Interval Arithmetic
    Triangulation

    Keywords

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

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    Verified Computations for Hyperbolic 3-Manifolds. / Hoffman, Neil; Ichihara, Kazuhiro; Kashiwagi, Masahide; Masai, Hidetoshi; Oishi, Shinichi; Takayasu, Akitoshi.

    In: Experimental Mathematics, Vol. 25, No. 1, 02.01.2016, p. 66-78.

    Research output: Contribution to journalArticle

    Hoffman, Neil ; Ichihara, Kazuhiro ; Kashiwagi, Masahide ; Masai, Hidetoshi ; Oishi, Shinichi ; Takayasu, Akitoshi. / Verified Computations for Hyperbolic 3-Manifolds. In: Experimental Mathematics. 2016 ; Vol. 25, No. 1. pp. 66-78.
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