Work
Thanks to Lefschetz and others, the cup product structure of cohomology was understood by the early 1940s. Steenrod was able to define operations from one cohomology group to another (the so-called Steenrod squares) that generalized the cup product. The additional structure made cohomology a finer invariant. The Steenrod cohomology operations form a (non-commutative) algebra under composition, known as the Steenrod algebra.
His book The Topology of Fibre Bundles is a standard reference. In collaboration with Samuel Eilenberg, he was a founder of the axiomatic approach to homology theory. See Eilenberg–Steenrod axioms.
Read more about this topic: Norman Steenrod
Famous quotes containing the word work:
“There never has been a time in our history when work was so abundant or when wages were as high, whether measured by the currency in which they are paid or by their power to supply the necessaries and comforts of life.”
—Benjamin Harrison (1833–1901)
“Even the wisest man grows tense
With some sort of violence
Before he can accomplish fate,
Know his work or choose his mate.
Poet and sculptor, do the work,
Nor let the modish painter shirk”
—William Butler Yeats (1865–1939)
“Man is a shrewd inventor, and is ever taking the hint of a new machine from his own structure, adapting some secret of his own anatomy in iron, wood, and leather, to some required function in the work of the world.”
—Ralph Waldo Emerson (1803–1882)