John Henry Constantine Whitehead

John Henry Constantine Whitehead (born November 11, 1904 in Madras , † May 8, 1960 in Princeton ), known as Henry Whitehead, was a British mathematician and one of the founders of the homotopy theory.

Live and act

Henry Whitehead was the son of the Bishop of Madras (now known as Chennai). His paternal uncle was the mathematician and philosopher Alfred North Whitehead . Whitehead grew up in Oxford with his grandmother from the age of one and a half, while his parents stayed in India until he was sixteen. He attended Eton College and then the Balliol College of the University of Oxford with a 1,923 won scholarship. After graduating, he worked as a stockbroker for a year, but then went back to Oxford University, where he was drawn to a lecture by Oswald Veblen on differential geometry and topology .

Henry Whitehead about 1934

In 1930 he received his doctorate from Veblen in Princeton (where he was from 1929 to 1932) and wrote the book Foundations of differential geometry (1932) with him , in which the concept of differentiable manifold was first developed. At Princeton he also worked with Solomon Lefschetz . In 1933 he became a Fellow of Balliol College in Oxford, where he held the Waynflete Professorship for Pure Mathematics from 1947. In 1944 he became a Fellow of the Royal Society . 1953 to 1955 he was President of the London Mathematical Society . He died unexpectedly of a heart attack in 1960 while visiting Princeton.

In the 1930s he helped many mathematicians persecuted in Germany (such as Max Dehn and Samuel Eilenberg ). Erwin Schrödinger lived with him for a while after going into exile in England. During the Second World War he worked for the Admiralty in the application of operations research methods against submarines and then in Bletchley Park on the deciphering of German secret codes (especially in a group led by Max Newman , the Newmanry , which deals with the Deciphering the Lorenz key addition ).

In 1935 he used the Whitehead entanglement that he had introduced to construct Whitehead manifolds , with which he corrected his attempt to prove the Poincaré conjecture of 1934 himself. More precisely, he tried in 1934 to prove that every open three-dimensional manifold that is contractible is homeomorphic to Euclidean space , which he then refuted with the counterexample of the Whitehead manifold.

He came up with the definition of a CW complex , which he introduced in two fundamental papers from 1949 ( Combinatorial Homotopy ). He demonstrated its importance by proving Whitehead's Theorem .

His student Ioan James published his collected works in four volumes in 1962/63. Two prizes from the London Mathematical Society are named after him: the annual Whitehead Prize and the Senior Whitehead Prize , awarded every two years .

In 1934 he married the concert pianist Barbara Smyth, a cousin of Peter Pears , with whom he had two sons.

Fonts (selection)

• On equivalent sets of elements in a free group. Ann. of Math. (2) 37 (1936), no. 4, 782-800.
• On C ¹ complexes. Ann. of Math. (2) 41, (1940), 809-824.
• Combinatorial homotopy , Bull. Amer. Math. Soc., Volume 55, 1949, 213-245 (part 1), Online , pp. 453-496 (part 2)
• Simple homotopy types. Amer. J. Math. 72, (1950), 1-57.
• with James: The homotopy theory of sphere bundles over spheres . Proc. London Math. Soc. (3); I: 4, 196-218 (1954); II: 5, 148-166 (1955).

literature

• Peter Hilton, Ioan James: The Whitehead Heritage , Mathematical Intelligencer 1997, No. 1

See also

• Whitehead-Serre theorem

Web links

• John J. O'Connor, Edmund F. Robertson :  John Henry Constantine Whitehead. In: MacTutor History of Mathematics archive .

Individual evidence

1. ↑ Whitehead, A certain open manifold whose group is unity , Quarterly journal of mathematics 6, 1935, pp. 268-279
2. ^ Whitehead, Certain theorems about three-dimensional manifolds (I) , Quarterly journal of mathematics, Volume 5, 1934, pp. 308-320
3. ^ John Milnor, The Poincare Conjecture, Clay Math. Inst., Pdf