Verified Computations for Hyperbolic 3-Manifolds

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)


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
Issue number1
Publication statusPublished - 2016 Jan 2


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

ASJC Scopus subject areas

  • Mathematics(all)


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