2 problems

Birman's injectivity conjecture. The monoid of singular braids maps injectively into the group algebra of the braid group.

Let $V^r$ be an invariant of $r$-singular knots. Say that $V^r$ is once-integrable if there is an invariant $V^{r-1}$ of $(r-1)$-singular knots whose derivative is $V^r$. Hutchings…