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Norman Steenrod

Norman Steenrod

American mathematician
The basics
Quick Facts
Intro American mathematician
A.K.A. Norman Earl Steenrod
Countries United States of America
Occupations Mathematician Topologist Educator
Gender male
Birth 22 April 1910 (Dayton)
Death 14 October 1971 (Princeton Township, New Jersey)
Education Harvard University, Princeton University, University of Michigan
The details
Biography

Norman Earl Steenrod (April 22, 1910 – October 14, 1971) was a mathematician most widely known for his contributions to the field of algebraic topology.

Life

He was born in Dayton, Ohio, and educated at Miami University and University of Michigan (A.B. 1932). After receiving a master's degree from Harvard University in 1934, he enrolled at Princeton University. He completed his Ph.D. under the direction of Solomon Lefschetz, with a thesis titled Universal homology groups. He held positions at the University of Chicago from 1939 to 1942, and the University of Michigan from 1942 to 1947. He moved to Princeton University in 1947, and remained on the Faculty there for the rest of his career. He died in Princeton.

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.

Publications

  • Steenrod, N. E. (1962), Epstein, D. B. A., ed., Cohomology operations, Annals of Mathematics Studies, 50, Princeton University Press, ISBN 978-0-691-07924-0, MR 0145525 

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