A stable range description of the space of link maps

Abstract

We study the space $Link\left(P,Q;N\right)$ of link maps: maps from $P\bigsqcup Q$ to $N$ such that the images of $P$ and $Q$ are disjoint. We identify the homotopy fiber of the inclusion $Link\left(P,Q;N\right)\to Map\left(P,N\right)\times Map\left(Q,N\right)$ in a stable range, showing that it has a $\left(2\left(n-p-q\right)-3\right)$–connected map to the infinite loopspace of a certain Thom spectrum.