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We develop invariants of the lower central series of free groups throughlinking of letters, showing they span the rational linear dual of the lowercentral series subquotients. We build on an approach to Lie coalgebras throughoperads, setting the stage for generalization to the lower central series Liealgebra of any group. Our approach yields a new co-basis for free Lie algebras.We compare with the classical approach of Fox derivatives. v2: substantialrefinement of exposition

Linking of letters and the lower central series of free groups