John Henry Constantine Whitehead (11 November 1904–8 May 1960), was one of the founders of modern algebraic topology. One of the founders of the influential journal Topology.
Not to be confused with George Whitehead, who also worked in algebraic topology.
His contributions to mathematics include the following:
CW complexes; these were introduced in his papers on
combinatorial homotopy, which in turn were one prime source of inspiration for Brown, Higgins and Sivera’s, Nonabelian Algebraic Topology and also for Baues’ extensive work on, for instance, Combinatorial Homotopy and 4-Dimensional Complexes;
the Whitehead group? which is a precursor of constructions in algebraic K-theory;
with Saunders Mac Lane, first characterisation of homotopy 2-types.
founder of the algebraic homotopy programme;
he introduced crossed modules
J. H. C. Whitehead, An expression of Hopf ’s invariant as an integral, Proc. Nat. Acad. Sci. U. S. A.33 (1947), 117–123 (jstor:87688)
(on the Hopf invariant)
J. H. C. Whitehead, Combinatorial homotopy I , Bull. Amer. Math. Soc, 55, (1949), 213–245.
J. H. C. Whitehead, Combinatorial Homotopy II, Bull.
Amer. Math. Soc., 55 (1949), 453–496.
(on homotopy theory via crossed modules)
J. H. C. Whitehead, Algebraic Homotopy Theory, in Proc. Int. Cong. of Mathematics, Harvard, volume 2, 354 – 357. 51 (1950)
(on homotopy theory)
J. H. C. Whitehead, Simple homotopy type, Amer. J. Math., 72, (1950), 1 - 57.
(on simple homotopy type).
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