3 problems

Odd-parameter pretzel conjecture. The knot $K$ is strongly quasipositive if and only if either $|d|=n$, or $|d|=n-2$ and, after possibly reordering so that…

Let $P$ be a pattern in the solid torus, let $K$ be a knot of genus $g$, let $U$ denote the unknot, and write $P(U,-n)$ for the pattern knot after $-n$ full twists. Satellite L-spa…

Let $P$ be a pattern in the solid torus, let $K$ be a knot, and let $U$ denote the unknot. Lidman–Vafaee's converse conjecture. Under conditions that the pattern is embedded “nicel…