April 22, 1910|
|Died||14 October 1971
Princeton, New Jersey
|Alma mater||University of Michigan
|Known for||Eilenberg–Steenrod axioms|
|Institutions||University of Chicago
University of Michigan
|Doctoral advisor||Solomon Lefschetz|
|Doctoral students||Peter Freyd
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.
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.
- Abstract nonsense
- Eilenberg–Steenrod axioms
- Fiber bundle
- Steenrod algebra
- Steenrod homology
- Steenrod operations
- Steenrod problem
- 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
- Steenrod, Norman, et al. First Concepts of Topology. The Mathematical Association of America New Mathematical Library. Miami: 1966.
- Milnor, John (1958). "Review: Norman Steenrod, The topology of fibre bundles". Bull. Amer. Math. Soc. 64 (4): 202–203. doi:10.1090/s0002-9904-1958-10211-6.
- Szczarba, R. H. (1964). "Review: Cohomology operations. Lectures by N. E. Steenrod. Written and revised by D. B. A. Epstein". Bull. Amer. Math. Soc. 70 (4): 482–483. doi:10.1090/s0002-9904-1964-11157-5.