8 problems

Knots in $S^3$ are related by ribbon concordance when there is a ribbon concordance between them. Gordon's conjecture. Ribbon concordance defines a partial order on knots in $S^3$.…

Ribbon homology cobordism monotonicity conjecture. If $Y_-$ and $Y_+$ are homology $3$-spheres and there is a ribbon homology cobordism from $Y_-$ to $Y_+$, then

Let $K$ be a knot in $S^3$, and write $J\leq K$ when the knot $J$ is ribbon concordant to $K$. Finite-predecessor conjecture. For each knot $K\subset S^3$, there are only finitely…

Let $K$ and $K'$ be knots in $S^3$, and write $K'\leq K$ when there is a ribbon concordance from $K$ to $K'$. A knot $K$ is positive if it admits an oriented diagram in which every…

Let $K$ and $K'$ be knots in $S^3$, and write $K'\leq K$ when there is a ribbon concordance from $K$ to $K'$. A knot $K$ is ribbon concordance minimal if $K'\leq K$ implies that…

Let $K_0,K_1\subset S^3$ be knots, and write $K_0\leq K_1$ when there is a ribbon concordance from $K_1$ to $K_0$. A knot is alternating if it admits a diagram in which over- and u…

Let $T(2,p)$ denote the $(2,p)$-torus knot, and let $K_p$ be its 2-twist spin. A knot is a root of the ribbon concordance graph if no distinct knot ribbon-concords to it from below…

Let $\geq_{\operatorname{top}}$ denote the topological ribbon concordance relation on knots. Topological ribbon concordance conjecture. The relation $\geq_{\operatorname{top}}$ is…