Cup Product

The cup product is a product on cohomology classes. In the case of de Rham cohomology, a cohomology class can be represented by a closed form. The cup product of  and  is represented by the closed form , where  is the wedge product of differential forms. It is the dual operation to intersection in homology.

In general, the cup product is a map

which satisfies , where  is the th cohomology group.