7 problems

Cochran–Orr conjecture. A link in $S^3$ is null $k$-cobordant if and only if all its Milnor $\overline{\mu}$-invariants of lengths $j$, $1\le j\le 2k$, are zero.

Let $n\geq 1$. Consider the ribbon link and its self-mutant described above, with all minimal linkings of weight at most $2n+7$ vanishing except for the specific $(2n+7)$-linking,…

Invariant agreement conjecture. For $\b7$-Brunnian embedded links, Koschorke's $\b7_\b7(f)$ coincides up to sign with $\b7(\b7(1),\ldots,\b7(d-1),d)$.

$k$-repeating higher-order Arf conjecture. The map $\mathrm{Arf}^k_j$ is an isomorphism for all $k$ and $j$. This is the $k$-repeating analogue of the higher-order Arf invariant co…

Let $m$ be a positive integer and let $d>3$. Consider the space of link maps … A product of Milnor invariants of type $n$ gives, via configuration-space integrals, a generalized Mi…

Boundary-link fusion conjecture. The class of links concordant to fusions of boundary links is equal to the class of links all of whose Milnor $\overline{\mu}$-invariants vanish.

Vanishing Milnor invariants conjecture. Every link with vanishing Milnor $\bar\mu$-invariants is an $\widehat F$-link.