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Geometric triangulations and highly twisted links

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arxiv 2005.11899 v3 pith:5ZNK2SEK submitted 2020-05-25 math.GT

Sophie L. Ham , Jessica S. Purcell This is my paper · ORCID
classification math.GT
keywords geometrichighlyhyperbolictriangulationtwistedadditionadmitadmits
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It is conjectured that every cusped hyperbolic 3-manifold admits a geometric triangulation, i.e. it is decomposed into positive volume ideal hyperbolic tetrahedra. Here, we show that sufficiently highly twisted knots admit a geometric triangulation. In addition, by extending work of Gueritaud and Schleimer, we also give quantified versions of this result for infinite families of examples.

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  1. Expansion joints in hyperbolic manifolds

    math.GT 2025-11 conditional novelty 7.0 of 10

    Cone-deforming an ideal arc through 'expansion joints' interpolates between stacked Borromean ring complements and lantern manifolds, and yields cone deformations of highly twisted 2-bridge unknotting tunnels.

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