2 problems

Let $K$ be a knot in $S^3$. An essential $2$–string tangle decomposition is one arising from a $2$–sphere intersecting $K$ transversely in four points such that the punctured spher…

Let $K$ be a knot in $S^3$. An essential tangle decomposition is an essential $n$–string tangle decomposition for some integer $n$, meaning that there is a $2$–sphere intersecting…