8 problems

Let $F\subset S^3$ be a quasipositive Seifert surface. A proper arc in $F$ is an arc with endpoints on $\partial F$ and interior in the interior of $F$. Let $A(O,-1)$ be the surfac…

Let $K$) and $L$ be prime knots, and let $S(K)$ and $S(L)$ denote their hosting sets. Hosting-set rigidity conjecture. If … then $K=L$. This asks whether a prime knot is determined…

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 $K$ be a knot, and let a slice derivative mean a derivative of $K$ that is slice in the relevant category. Generalised Kauffman conjecture. If $K$ is a topologically (respectiv…

Kauffman's conjecture. There exists an essential simple closed curve $d$ on $F$ such that

Let $K$ be a slice knot. A Seifert surface $F$ stabilizes to a Seifert surface $F'$ if $F'$ is obtained from $F$ by finitely many trivial one-handle attachments. A Levine surface i…

Let $K$ be a slice knot, and let $F$ be a genus-one Seifert surface for $K$. For a simple closed curve $d$ on $F$, write $d^+$ for its positive push-off and…

A knot is a smooth embedding $\mathbb{S}^1\hookrightarrow\mathbb{S}^3=\partial\mathbb{B}^4$. It is slice if it bounds a smoothly embedded disk in $\mathbb{B}^4$. A genus one Seifer…