Verified computations for hyperbolic 3-manifolds
Geometric Topology
2013-12-02 v2
Abstract
For a given cusped 3-manifold admitting an ideal triangulation, we describe a method to rigorously prove that either or a filling of 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.
Cite
@article{arxiv.1310.3410,
title = {Verified computations for hyperbolic 3-manifolds},
author = {Neil Hoffman and Kazuhiro Ichihara and Masahide Kashiwagi and Hidetoshi Masai and Shin'ichi Oishi and Akitoshi Takayasu},
journal= {arXiv preprint arXiv:1310.3410},
year = {2013}
}
Comments
27 pages, 3 figures. Version 2 has minor changes, mostly attributed to a small simplification of the code associated to this paper and the correction of typographical errors