k-reduced groups and Milnor invariants

Abstract

We characterize, in an algebraic and in a diagrammatic way, Milnor string link invariants indexed by sequences where any index appears at most k times, for any fixed k ≥ 1. The algebraic characterization is given in terms of an Artin-like action on the so-called k-reduced free groups; the diagrammatic characterization uses the langage of welded knot theory. The link case is also addressed.