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Sophie L. Ham

Publications and source records attributed to Sophie L. Ham.

2 recordsLinked to original sources
arXiv2023

Canonical triangulations of Dehn fillings of the Borromean rings link complement

The set of canonical decompositions of a cusped hyperbolic 3-manifold is a complete topological invariant. However, there are only a handful of infinite families for which canonical decompositions are known. In this paper, we find canonical triangulations for Dehn fillings of the Borromean rings link complement and two related manifolds obtained by half-twists. The underlying triangulations were shown to be geometric by Ham and Purcell. To obtain canonical triangulations, we show a local convexity result at every face of the geometric triangulation.

math.GT↗
arXiv2021

Geometric triangulations and highly twisted links

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.

math.GT↗