4 problems

Let $f:S^1\sqcup\dots\sqcup S^1\to\mathbb{R}^3$ be any map. Circle-map homotopic disjoinability conjecture. Every such map is homotopically disjoinable. Here homotopically disjoina…

Massey–Rolfsen conjecture. Theorem still holds if one component of the link $L$ is not embedded (but mapped into $\mathbb{R}^4$ disjointly from the other components).

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

Kirk–Livingston's infinite-rank conjecture. The group of type $2$ invariants in the Kirk–Livingston sense has infinite rank for $2$-component links with any linking number.