Verified computations for hyperbolic 3-manifolds

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 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.

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

References in corpus (1)

• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds

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