3 problems

Main Conjecture. A spatial graph $G$ has a finite $N$-quandle if and only if there is a spherical orbifold with underlying space $\mathbb{S}^3$ whose singular locus is the edge-lab…

Mellor–Smith classification conjecture. Every labeled link with finite $N$-quandle is the singular locus of a spherical orbifold with underlying space $\mathbb{S}^3$ appearing in D…

Let $Q$ be a hyperbolic $3$-orbifold. A $(2,4,6)$ turnover is a turnover with cone-point orders $2$, $4$, and $6$; it is immersed, non-embedded if its immersion into $Q$ is not an…