Abstract: How can you tell if some word is an n-fold commutator? How do cochains “see” the fundamental group? We give explicit answers to these questions, in work in progress with N. Gadish, A. Ozbek and B. Walter. In particular, we take an abstract isomorphism between the dual of the zeroth Harrison homology of rational cochains of a space with the Malcev completion of its fundamental group, established by U. Buijs, Y. Felix, A Murillo and D. Tanre, and show it is realized through Hopf invariants. We thus complete a program initiated by B. Walter and myself to explicitly construct “homotopy periods” on nilpotent spaces. When the space is a two-complex, the resulting “letter linking” invariants for words are defined for all finitely presented groups, a result which has not been achieved for other explicit funcationals, namely those arising from Magnus expansion and Fox calculus. We outline a planned application to Milnor’s link invariants, showing how different choices of Seifert surfaces can lead to either Cochran’s approach or diagrammatic formulae.