3 papers
math.GT2025
On Geometric triangulations of double twist knots
Dionne Ibarra, Daniel V. Mathews, Jessica S. Purcell
In this paper we construct two different explicit triangulations of the family of double twist knots using methods of triangulating Dehn fillings, with layered solid tori…
math.GT2024
Triangulations of the 3-sphere with knotted edge
Dionne Ibarra, Daniel V. Mathews, Jessica S. Purcell +1
We prove that for any knot , there exists a one-vertex triangulation of the -sphere containing an edge forming . The proof is constructive, and based on fully augmented li…
math.GT2024
Lambda lengths in The figure eight knot complement
Joshua A. Howie, Dionne Ibarra, Daniel V. Mathews +1
In the complete hyperbolic structure on the complement of the figure eight knot, we determine the set of lambda lengths from the maximal cusp to itself. Using the correspondence be…