nLab J.H.C. Whitehead

John Henry Constantine Whitehead (11 November 1904–8 May 1960), was one of the founders of modern algebraic topology. Also one of the founders of the influential journal Topology.

• Wikipedia entry

• MacTutor biography

Not to be confused with George Whitehead, who also worked in algebraic topology.

Contributions

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;

• simple homotopy theory;

• 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;

• Whitehead product

• Whitehead theorem

• he introduced crossed modules

Selected writings

On the triangulation theorem for smooth manifolds:

• J. H. C. Whitehead, On $C^1$-complexes, Ann. of Math. (2) 41 (1940), 809–824 (doi:10.2307/1968861, jstor:1968861)

On the Hopf invariant:

• 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)

Proving the Whitehead theorem andntroducing crossed modules (and their crossed homomorphisms) as models for homotopy types:

• J. H. C. Whitehead, Combinatorial homotopy. I, Bulletin of the American Mathematical Society 55 3 (1949) 213–245 [doi:10.1090/s0002-9904-1949-09175-9, pdf]

• J. H. C. Whitehead, Combinatorial Homotopy II, Bull. Amer. Math. Soc., 55, (1949), 453 – 496 (euclid:1183513797)

On homotopy theory:

• J. H. C. Whitehead, Algebraic Homotopy Theory, in Proc. Int. Cong. of Mathematics, Harvard, volume 2, 354 – 357. 51 (1950)

On simple homotopy type:

• J. H. C. Whitehead, Simple homotopy type, Amer. J. Math., 72, (1950), 1 - 57.

category: people