4 problems

Let $K\subset\mathbb{S}^3$ be a hyperbolic knot, and let $\mathbb{S}^3\setminus K$ denote its complement. The complement has hidden symmetries when a homeomorphism between finite-d…

For $R>0$, consider hyperbolic knot complements in $\mathbb{S}^3$ with hidden symmetries and volume less than $R$. Finiteness conjecture. For any $R>0$, at most finitely many hyper…

Finite-volume hidden-symmetry conjecture. There are at most finitely many hyperbolic knot complements with hidden symmetries and volume less than $v$.

Finiteness conjecture. For any $R>0$, at most finitely many hyperbolic knot complements have hidden symmetries and volume less than $R$.