The Massey–Rolfsen conjecture for links with one nonembedded component

Let $L\colon S^2\amalg\dots\amalg S^2\to\mathbb{R}^4$ be a link whose components have pairwise disjoint images, with at most one component not embedded. The link is link homotopic to the unlink.

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).

This extends the asserted null-homotopy result from smooth embedded links to links with one possibly self-intersecting component. The source notes that the two-component case follows from work of Teichner, while the general case is presented as a conjecture.