Three-component link-map connectivity conjecture

Let $P_1$, $P_2$, and $P_3$ be manifolds of dimensions $p_1$, $p_2$, and $p_3$, respectively, and let $N$ be an $n$-dimensional manifold. For a basepoint in the image of $\operatorname{Link}(P_1,P_2,P_3;N)$, let $l_3$ be the map from the homotopy fiber of the comparison with $\mathcal{T}_2\operatorname{Link}(P_1,P_2,P_3;N)$ to the loop space of the corresponding cobordism space.

Three-component connectivity conjecture. The map $l_3$ is $(3n-\max\{2p_1+p_2+p_3,p_1+2p_2+p_3,p_1+p_2+2p_3\}-5)$-connected.

The source presents this as an analogue of the two-component connectivity conjecture and says that a future paper will address it. No resolution is given.