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:
“In poorer lands
No one touches the water of life.
It has no taste
And though it refreshes absolutely
It is a cup that must also pass
Until everybody
Gets some advantage....”
—John Ashbery (b. 1927)
“The guys who fear becoming fathers don’t understand that fathering is not something perfect men do, but something that perfects the man. The end product of child raising is not the child but the parent.”
—Frank Pittman (20th century)