7 problems

Let $K$ be a knot. A knot is cabled when it is a nontrivial cable knot. In the notation of the source, let $b_i$ be the linear coefficient associated with a Jones slope in the quad…

Let a weight system be associated with a Vassiliev invariant, and let the natural cabling operation on knots have an order parameter. Cabling-order conjecture. The order of the nat…

Let $K$ be a knot with a well-defined GM series, and let $C_{(tp,sp)}(K)$ denote its $(tp,sp)$-cabling with $\gcd(s,t)=1$. Cabling Formula. The cabling formula above holds for any…

The $(n,1)$-cable conjecture. For all $n\geq 2$,

Let $K$ be a knot, let $p$ and $q$ be relatively prime integers with $|p|>1$, and let $K_{p,q}$ denote the $(p,q)$-cable of $K$. Let $\mathcal{C}$ denote the smooth knot concordanc…

Let $K$ be a knot, and suppose that in the relevant degree quasi-polynomial the coefficient $b_1$ vanishes. Cabling conjecture. When $b_1=0$, $K$ is cabled. The source gives this a…

Let $K_1$ and $K_2$ be non-isotopic simple knots. For integers $p$ and $q$, the cable-detection conjecture asserts that there exist numbers $p$ and $q$ such that the $(p,q)$-cables…