Verified computations for hyperbolic 3-manifolds
Date
2013-10-12Author
Hoffman, Neil
Ichihara, Kazuhiro
Kashiwagi, Masahide
Masai, Hidetoshi
Oishi, Shin'ichi
Takayasu, Akitoshi
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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 are an implementation of interval arithmetic and Krawczyk's 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.
Citation
Hoffman, N., Ichihara, K., Kashiwagi, M., Masai, H., Oishi, S., Takayasu, A. (2013). Verified computations for hyperbolic 3-manifolds.