Homotopy classes of 2 disjoint 2p-spheres in R3p + 1

For p ≠ 3,7, p > 1, link homotopy classes of link maps S2p ⊔ S2p → S3p + 1 are classified using the α-invariant. It is shown that any such link map is link homotopic to an embedded link. These results are obtained through a study of the homotopy type of the complement of the image of a map from one sphere to another.