Massey product

Summary

A Massey product is a secondary operation on cohomology. It takes three classes $u, v, w$ with $uv = 0$ and $vw = 0$ and produces a set of classes of degree one less than that of $u v w$. It is defined from the cup product on cochains, not just on cohomology. Massey products detect structure that the cohomology ring alone does not see, such as the linking of the Borromean rings.