triple product to prove that the Whitehead product satisfies the Jacobi identity. Massey products of higher order appear when computing twisted K-theory by means of the Atiyah–Hirzebruch spectral sequence (AHSS). In particular, if H is the twist 3-class, showed that, rationally, the higher order differentials in the AHSS acting on a class x are given by the Massey product of p copies of H with a single copy of x. If a manifold is (in the sense of Dennis Sullivan), then all Massey products on the space must vanish; thus, one strategy for showing that a given manifold is formal is to exhibit a non-trivial Massey product. Here a formal manifold is one whose rational homotopy type can be deduced ("formally") from a finite-dimensional "minimal model" of its de Rham complex. showed that compact Kähler manifolds are formal. use a Massey product to show that the homotopy type of the configuration space of two points in a lens space depends non-trivially on the simple homotopy type of the lens space. See also Toda bracket References External links Massey products and its applications - contains many explicit examples Massey products in the Adams Spectral Sequence - contains references useful for understanding how to do these computations An Adams Spectral Sequence Primer - Bruner's notes Massey products and A-infinity structures Algebraic topology Differential topology Ternary operations