5 problems

Let $K$) be a non-trivial knot, and let $W(K)$ be a Whitehead double of $K$. The Kidwell–Stoimenow conjecture. Is it always the case that … Kidwell and Stoimenow reported that the…

Let $K$ be a knot, let $W_K$ be its Whitehead double, and let $F(K)$ be the Kauffman polynomial of $K$ in the variables $a$ and $z$. Stoimenow–Kidwell conjecture. Then … The questi…

Let $K$) be a knot, let $D(K)$ denote its positively-clasped Whitehead double, and let $[K]$ and $[D(K)]$ denote their elements in the knot concordance group $\mathcal{C}$. Kirby’s…

Let $K$ be a prime knot, let $c(K)$ denote its crossing number, and let $W(K)$ be its Whitehead double. Jang–Lee's conjecture. The crossing number of any prime knot coincides with…

Let $T_{2,3}$ be the $(2,3)$ torus knot, and let $D(K)$ denote its positively-clasped untwisted Whitehead double. Two knots are smoothly concordant when their connected sum with on…