7 problems

Solvable-filtration conjecture.

Let $\cF_n$ denote the $n$-solvable subgroup of the topological knot concordance group, and let $\cF_{n.5}$ denote the $(n+0.5)$-solvable subgroup, for an integer $n\ge 0$. The ass…

Let $\mathcal{C}$ be the topological concordance group of knots in $S^3$, let $\widehat{\mathcal{C}}$ be the corresponding concordance group of knots in homology spheres, and let…

Let $K$ be a knot, let $n\in \frac{1}{2}\mathbb{N}_0$, and let an $(n)$-solvable derivative mean a derivative of $K$ that is $(n)$-solvable. Solvable Kauffman conjecture. For every…

Let $K$ admit a genus-one Seifert surface and a derivative $J$; consequently, $J$ is a knot and … Suppose $m\notin\{0,-1\}$. Genus-one derivative conjecture. The algebraic concorda…

Let $K$ be a knot, let $J$ be a derivative associated to an $(n+1)$-solution for $K$, where $n$ is a non-negative integer or half-integer, and let $Delta_K(t)$ denote the Alexander…

Intersection conjecture. It is conjectured that