Title: Cocycles of nilpotent quotients of free groups,
Abstract: We focus on the cohomology of the $k$-th nilpotent quotient of the free
group, $F/F_k$. This paper describes all the group 2-, 3-cocycles in terms of
Massey products, and gives expressions for some of the 3-cocycles. We also give
simple proofs of some of the results on Milnor invariants and the
Johnson-Morita homomorphisms.