A generalization of Milnor's μ-invariants to higher-dimensional link maps

Abstract

In this paper we generalize Milnor's μ-invariants (which were originally defined for “almost trivial” classical links in R 3) to (a corresponding large class of) link maps in arbitrary higher dimensions. The resulting invariants play a central role in link homotopy classification theory. They turn out to be often even compatible with singular link concordances. Moreover, we compare them to linking coefficients of embedded links and to related invariants of Turaev and Nezhinskij. Along the way we also study certain auxiliary but important “Hopf homomorphisms”.