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:
“The cup of Morgan Fay is shattered.
Life is a bitter sage,
And we are weary infants
In a palsied age.”
—Allen Tate (1899–1979)
“To [secure] to each labourer the whole product of his labour, or as nearly as possible, is a most worthy object of any good government.”
—Abraham Lincoln (1809–1865)