2 problems

Let $M$ be a $3$-manifold, let $\pi_1(M)_{r}^{(n)}$ denote the $n$th term of its rational derived series, and define … For each $n\in\mathbb{N}$, let $||\\,\cdot\\,||_n$ be the cor…

Existence conjecture. For each $n\geq 0$ there exist knots $K$ and $K_*$ such that $\mathcal{A}_i(K)\cong\mathcal{A}_i(K_*)$ for $0\leq i<n$, but