4 problems

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…

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 $J$ be a knot with bridge spectrum … and let $K={\mathsf {cable}}(T_{m,n},J)$ be a cable of $J$. The bridge-spectrum cabling conjecture. … The conjecture expresses the observed…

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…