Core-edge conjecture for one-vertex triangulations of lens spaces

A lens space is a 3-manifold obtained by gluing together two solid tori. A core edge in a one-vertex triangulation is an edge that realizes a core curve of one of the solid tori, meaning that the complement of a regular neighbourhood of the corresponding embedded closed curve is a solid torus.

Core-edge conjecture. Every one-vertex triangulation of a lens space has a core edge.

This conjecture asks whether the topology of a lens space is always detected by an edge in every one-vertex triangulation. The paper presents it as one of three conjectures motivating its search for counterexamples; its status is not resolved in the supplied text.