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