 Cup product

The cup product is a natural bilinear operation $H^p(X;R)\times H^q(X;R)\to H^{p+q}(X;R)$. It is graded-commutative: $a⌣b=(-1{)}^{pq}b⌣a$.

In algebraic topology, the cup product is a binary operation on the cohomology groups of a topological space. It provides a way to combine cohomology classes to produce new cohomology classes, thereby enriching our understanding of the topology of the space.