We construct a sequence of concordanceinvariants for classical links, which depend on the peripheral isomorphism typeof the nilpotent quotients of the link fundamental group. The terminology stemsfrom the fact that we replace the Magnus expansion in the definition of Milnor's$\bar{\mu}$-invariants by the similar Campbell–Hausdorff expansion. Themain point is that we introduce a new universal indeterminacy, which depends onlyon the number of components of the link. The Campbell–Hausdorff invariantsare new, effectively computable and can efficiently distinguish (unordered andunoriented) isotopy types of links, as we indicate on several families of closedbraid examples. They also satisfy certain natural dependence relations, whichgeneralize well-known symmetries of the $\bar{\mu}$-invariants.

1991Mathematics Subject Classification: 81S25, 46L10, 46L50, 47A60.