(no subject)

The cup product in the simplicial cochain complex is supercommutative modulo terms depending on a "derived" product of degree -1. That new product is anti-supercommutative modulo terms depending on a product of degree -2. Et cetera. The formula for the cup product is in every textbook on algebraic topology. The formula for the degree -1 product is in a 1947 paper by Steenrod in Ann. Math. He defines all higher products, but does not give an explicit formula for them. Anybody knows an explicit formula for the degree -2 product?