Binary operations | Homology theory | Algebraic topology

Cup product

In mathematics, specifically in algebraic topology, the cup product is a method of adjoining two cocycles of degree p and q to form a composite cocycle of degree p + q. This defines an associative (and distributive) graded commutative product operation in cohomology, turning the cohomology of a space X into a graded ring, H∗(X), called the cohomology ring. The cup product was introduced in work of J. W. Alexander, Eduard Čech and Hassler Whitney from 1935–1938, and, in full generality, by Samuel Eilenberg in 1944. (Wikipedia).

Cup product
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Wedge product | Cohomology ring | Topological space | Samuel Eilenberg | Cocycle | Hassler Whitney | Linking number | Massey product | Algebraic topology | Transversality (mathematics) | Chain complex | Homomorphism | Simplex | De Rham cohomology | Poincaré duality | Singular homology | Mathematics | Ring homomorphism | Embedding | Functor | Cap product | Closed and exact differential forms | Graded ring | Diagonal functor | Cohomology operation