George W. Whitehead

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George William Whitehead (born August 2, 1918 in Bloomington , Illinois , † April 12, 2004 ) was an American mathematician who dealt with topology .

George Whitehead studied at the University of Chicago , where he received his doctorate in 1941 under Norman Steenrod ( Homotopy properties of the real orthogonal groups ). He then was an instructor at Purdue University and Princeton University and an assistant professor at Brown University before becoming a professor at the Massachusetts Institute of Technology in 1949 . There he received a full professorship in 1957 and retired in 1985.

Whitehead was one of the pioneers of algebraic topology and homotopy theory . In the 1950s he applied spectral sequences early on to study the homotopy groups of spheres (independently of Jean-Pierre Serre and Henri Cartan in France). In 1942 he introduced the J-homormorphism from homotopy groups of the special orthogonal groups to the homotopy groups of spheres as an extension of a construction by Heinz Hopf . His 1962 article Generalized Homology Theories was particularly influential .

In 1972 he became a member of the National Academy of Sciences and in 1954 of the American Academy of Arts and Sciences . He was a Guggenheim Fellow and 1955/56 Fulbright Research Scholar. In 1962 he was invited speaker at the International Congress of Mathematicians in Stockholm ( Some aspects of stable homotopy theory ).

His PhD students include Robert Aumann and John Coleman Moore .

It should not be confused with John Henry Constantine Whitehead , after whom the Whitehead lemma , which leads to the definition of the K 1 group , and the Whitehead theorem , which characterizes the homotopy equivalence between CW complexes , are named.

Fonts

  • Recent advances in homotopy theory , American Mathematical Society 1970
  • Elements of homotopy theory , Springer Verlag, Graduate Texts in Mathematics, 1978
  • Homotopy Theory , MIT Press 1966
  • Homotopy groups of spheres. Proceedings of the International Congress of Mathematicians, Cambridge, Mass., 1950, vol. 2, pp. 358-362. Amer. Math. Soc., Providence, RI, 1952.
  • A generalization of the Hopf invariant. Ann. of Math. (2) 51: 192-237 (1950).
  • Generalized homology theories. Trans. Amer. Math. Soc. 102: 227-283 (1962).

Web links

Individual evidence

  1. ↑ George W. Whitehead in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used Template: MathGenealogyProject / Maintenance / name used
  2. ^ Whitehead On the homotopy groups of spheres and rotation groups , Annals of Mathematics, 2nd Series, Volume 43, 1942, pp. 634-640
  3. ↑ Trans. Amer. Math. Soc., Vol. 10, 1962, pp. 227-282
personal data
SURNAME Whitehead, George W.
ALTERNATIVE NAMES Whitehead, George William (full name)
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH August 2, 1918
PLACE OF BIRTH Bloomington , Illinois
DATE OF DEATH April 12, 2004