3 papers
math.GT2025
Augmented links, shadow links, and the TV volume conjecture: a geometric perspective
Dionne Ibarra, Emma N. McQuire, Jessica S. Purcell
For hyperbolic 3-manifolds, the growth rate of their Turaev-Viro invariants, evaluated at a certain root of unity, is conjectured to give the hyperbolic volume of the manifold. Thi…
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…