Norman Steenrod

Norman Earl Steenrod ( born April 22, 1910 in Dayton, Ohio, † October 14, 1971 in Princeton ( New Jersey)) was an American mathematician who was one of the founders of modern algebraic topology.

Life

Steenrods parents were teachers - his father was a teacher of technical drawing ( and incidentally amateur astronomer ), his mother a music teacher. Since he was an excellent student, he already did 15 years his high school degree and then worked for two years as an industrial designer, the profession of his elder brother, where he earned the money for his studies. In 1927 he went to the "University of Miami " in Oxford, Ohio and then to the University of Michigan in Ann Arbor, where he studied physics, philosophy and business and incidentally attended a course on topology at Raymond Wilder. After graduating in 1932, he first lived with his parents in Dayton and wrote a work in topology, which earned him scholarship offers from Harvard and Princeton ( next he earned money again as a designer at Chevrolet ). In 1934 he made ​​first at Harvard University with a master's degree and then went to the topologists Wilder and Solomon Lefschetz at Princeton University, where he worked in 1936 received his doctorate ( "Universal homology groups" ) and then as an assistant ( " Instructor "). In 1939 he went to the University of Chicago and in 1942 returned to the University of Michigan before he became in 1947 Professor at Princeton, where he remained until his retirement.

Among his doctoral students include Peter Freyd, Paul A. Schweitzer, Franklin Paul Peterson, Edwin Spaniards and William Massey ( Massey Spaniards and published known textbooks of algebraic topology).

In 1938, he married Carolyn Witter, with whom he had a son and a daughter.

Work

In a basic thesis was carried out in 1942 his " Steenrod cohomology operations " ( " Steenrod squares " ) on cohomology groups a, as a generalization of their behavior under the cup product of spaces (which already Lefschetz treated ), and examined their algebra ( " Steenrod Algebra " ) in composition. With a development of this Kohomologieoperatoren by José Adem John Frank Adams was later the problem of counting out of vector fields on spheres solve ( results to published Steenrod with Whitehead in the Proceedings of the National Academy of 1951). Steenrods lectures on it were much later published in 1962 as " Cohomology Operations " (edited by David Epstein ). With Samuel Eilenberg in 1952 he wrote the textbook " Algebraic Topology ", in which, inter alia, the homology theory with the " Eilenberg - Steenrod axioms '' is axiomatically justified and so the many developed until the late 1940s homology theories of Vietoris, Čech, among others were unified. Steenrod was also a pioneer in the study of fiber bundles ( " Fibre bundles " ), about which he wrote one of the first textbooks ( " Topology of Fibre bundles ", Princeton 1951).

With Sumner Byron Myers 1939 he proved the theorem of Steenrod -Myers.

Steenrod also wrote several volumes, "Reviews of papers in algebraic and differential topology, topological groups and homological algebra " (1968), "First concepts in Topology " (1966, with W. Chinn ), "Advanced Calculus " (van Nostrand 1959, with Donald C. Spencer, Nickerson ), " How to write mathematics" (American Mathematical Society, 1981)

Steenrod was a member of the National Academy of Sciences of the United States. He held the 1957 Colloquium Lectures of the American Mathematical Society (" Cohomology Operations " ) and 1958 a plenary lecture at the International Congress of Mathematicians in Edinburgh ( " Cohomology operations and symmetry products" ). In 1958 he gave a plenary lecture at the International Congress of Mathematicians in Edinburgh ( Cohomology operations and symmetric products ).

Writings

• With Samuel Eilenberg Foundations of Algebraic Topology, Princeton University Press 1952
• Cohomology Operations (Lectures by Norman Steenrod, written and revised by Epstein BA ), Princeton University Press 1962
• The Topology of Fibre Bundles, Princeton University Press 1951
• Cohomology operations derived from the symmetry group. In: Commentarii Mathematici Helvetici. Volume 31, 1956 / 1957.