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:
“I believe that water is the only drink for a wise man: wine is not so noble a liquor; and think of dashing the hopes of a morning with a cup of warm coffee, or of an evening with a dish of tea! Ah, how low I fall when I am tempted by them! Even music may be intoxicating. Such apparently slight causes destroyed Greece and Rome, and will destroy England and America.”
—Henry David Thoreau (1817–1862)
“The history is always the same the product is always different and the history interests more than the product. More, that is, more. Yes. But if the product was not different the history which is the same would not be more interesting.”
—Gertrude Stein (1874–1946)