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.
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Famous quotes containing the words cup and/or product:
“It is surely easier to confess a murder over a cup of coffee than in front of a jury.”
—Friedrich Dürrenmatt (1921–1990)
“Everything that is beautiful and noble is the product of reason and calculation.”
—Charles Baudelaire (1821–1867)