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.
Read more about Cup Product: Definition, Properties, Interpretation, Examples, Massey Products
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 (19211990)
“The site of the true bottomless financial pit is the toy store. Its amazing how much a few pieces of plastic and paper will sell for if the purchasers are parents or grandparent, especially when the manufacturers claim their product improves a childs intellectual or physical development.”
—Lawrence Kutner (20th century)