Homotopy string links and the κ-invariant

Koschorke introduced a map from the space of closed n-component links to the space of maps from the n-torus to the ordered configuration space of n-tuples of points in R3. He conjectured that this map separates homotopy links. The purpose of this paper is to construct an analogous map for string links, and to prove (1) this map in fact separates homotopy string links, and (2) Koschorke's original map factors through the map constructed here together with an analog of Markov's closure map defined on the level of certain function spaces.