3 problems

Habiro's conjecture. Two links in $M$ are equivalent if and only if they are $C_{\infty}^M$-equivalent.

Let $L(m)$ denote the string links on $m$ strands. For $n\geq 1$, let $V_n$-equivalence be the equivalence relation induced by the Vassiliev filtration, and let $C_n$-equivalence b…

$Y_\infty$-equivalence conjecture. Two $3$-manifolds are orientation-preserving homeomorphic if and only if they are $Y_\infty$-equivalent.