6 problems

Let $q>1$ and let $(L,\varphi)$ be an $F_m$-link concordance class in $C_{2q+1}(F_m)$. For each positive integer $k$, let $R_k(F_m)$ denote the space of $k$-dimensional unitary rep…

A knot is ribbon minimal if it is minimal under ribbon concordance, and a link is ribbon concordance minimal if it is minimal under ribbon concordance. Component-separation conject…

Let $K$ be a knot in $S^3$, and let $\mu_K$ be a meridian of $K$. Define the two-component link … A link is ribbon concordance minimal if it has no strictly smaller link under ribb…

Let $W_4$ denote the 4-twisted Whitehead link, a two-component link formed from the fourth twist knot and an unknot. Ribbon minimality conjecture. The link $W_4$ is ribbon minimal.…

Conway coefficient sign conjecture. The conclusion of the two-component obstruction holds whenever $L\in\mathcal{P}_0$: in general, the sign $(-1)^k$ is replaced by $(-1)^{s(k,m)}$…

Let $\mathcal{T}_n$ be the tree group of order $n$, let $\text{\sf W}_n$ be the corresponding graded group of link concordance classes, and set…