Norman Steenrod

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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

Steenrod's parents were teachers, his father a technical drawing teacher (and an amateur astronomer), and his mother a music teacher. Being an excellent student, he graduated from high school at the age of 15 and then worked for two years as an industrial designer, his older brother's profession, where he earned the money for his studies.

In 1927 he went to Miami University in Oxford in Ohio and then to the University of Michigan in Ann Arbor , where he studied physics, philosophy and economics and also attended a course on topology with Raymond Wilder . After graduating in 1932, he lived with his parents in Dayton and wrote a thesis in topology, which brought him scholarship offers from Harvard University and Princeton University (he also earned money as a designer at Chevrolet ). In 1934 he made his master's degree at Harvard University and then went to the topologists Wilder and Solomon Lefschetz at Princeton University, where he earned his doctorate in 1936 ("Universal homology groups") and then worked as an assistant ("Instructor").

In 1939 he went to the University of Chicago and in 1942 again to the University of Michigan, before becoming a professor at Princeton in 1947, where he remained until his retirement.

His doctoral students include Peter Freyd , Paul A. Schweitzer , Franklin Paul Peterson , Edwin Spanier, and William S. Massey (Spanier and Massey published well-known textbooks on algebraic topology).

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

plant

In 1942 he introduced his “Steenrod cohomology operations ” (“Steenrod squares”) on cohomology groups in a fundamental work , as a generalization of their behavior under the cup product (which Lefschetz already discussed), and examined their algebra (“ Steenrod algebra “) In composition. With a further development of these cohomology operators by José Ádem , John Frank Adams was later able to solve the problem of counting vector fields on spheres (Steenrod published results on this with Whitehead in the Proceedings of the National Academy of 1951). Steenrod's lectures on it were published much later in 1962 as Cohomology Operations (edited by David Epstein ). With Samuel Eilenberg he wrote the textbook "Algebraic Topology" in 1952, in which u. a. the homology theory is axiomatically justified with the " Eilenberg-Steenrod axioms " and thus the many different homology theories developed by Vietoris, Čech and others until the end of the 1940s. a. have been unified. Steenrod was also a pioneer in the study of fiber bundles ("Fiber bundles"), about which he wrote one of the first textbooks ("Topology of Fiber bundles", Princeton 1951).

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

Steenrod also wrote multi-volume "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 had been a member of the US National Academy of Sciences since 1956 . In 1957 he gave the Colloquium Lectures of the American Mathematical Society ("Cohomology Operations") and in 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).

Fonts

  • The Topology of Fiber Bundles (= Princeton Mathematical Series. 14, ISSN  0079-5194 ). Princeton University Press, Princeton NJ 1951.
  • with Samuel Eilenberg : Foundations of algebraic topology (= Princeton Mathematical Series. 15, ISSN  0079-5194 ). Princeton University Press, Princeton NJ 1952.
  • Cohomology operations derived from the symmetryc group. In: Commentarii Mathematici Helvetici . Volume 31, 1956/1957, pp. 195-218 .
  • Cohomology Operations. Lectures (= Annals of Mathematics Studies. 50, ISSN  0066-2313 ). Written and revised by DBA Epstein . Princeton University Press, Princeton NJ 1962.

literature

  • George Whitehead: The work of Norman E. Steenrod in algebraic topology: An appreciation. In: Franklin P. Peterson (Ed.): The Steenrod algebra and its applications: a conference to celebrate NE Steenrod's sixtieth birthday. Proceedings of the Conference held at the Battelle Memorial Institute, Columbus, Ohio March 30th – April 4th, 1970 (= Lecture Notes in Mathematics . 168). Springer, Berlin et al. 1970, ISBN 3-540-05300-X , pp. 1-10.

Web links

personal data
SURNAME Steenrod, Norman
ALTERNATIVE NAMES Steenrod, Norman Earl (full name)
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH April 22, 1910
PLACE OF BIRTH Dayton
DATE OF DEATH October 14, 1971
Place of death Princeton