Link maps and the geometry of their invariants

The geometry of two types of link homotopy invariants of a link map f:S^pS^qS^m is discussed. The first one is the -invariant which greatly generalizes the classical notion of linking number. The second one, the -invariant, is closely related to the linking behaviour of f|s^p with only the double point set of f|S^q, and therefore measures (to some extend) the obstruction to embedding S^q. These invariants are related by a Hopf invariant homomorphism. In many cases link maps are classified up to link homotopy here, and a setting is provided e.g. for future injectivity results for . Also the image of is studied, yielding an interesting double filtration of stable homotopy groups of spheres.