Connectivity conjecture for the two-component link-map comparison map

Let $P_1$ and $P_2$ be manifolds of dimensions $p$ and $q$, respectively, and let $N$ be an $n$-dimensional manifold. Write $\operatorname{Link}(P_1,P_2;N)$ for the space of link maps, and let $\mathcal{T}_2\operatorname{Link}(P_1,P_2;N)$ denote its second Taylor approximation. When the basepoint lies in the image of the space of link maps, let $l_2$ be the associated map from the homotopy fiber of the comparison map to the relevant cobordism loop space.

Connectivity conjecture. The map $l_2$ is $(2n-\max\{2p+q,2q+p\}-3)$-connected.

This conjecture gives the expected connectivity of the manifold-calculus comparison map for two-component link maps. The source states it as a consequence of the corresponding conjecture for the map from the link-map space to its second Taylor approximation; its resolution is not specified here.