User:Ambrose H. Field/sandbox

%% [text from here to ***************** is content of the article below the data box]

Charles Ehresmann (19 April 1905 – 22 September 1979) was a French mathematician who worked in differential topology and category theory. He was an early member of the Bourbaki group, and is known for his work on the work on the differential geometry of smooth fiber bundles, notably the jet concept (see jet bundle), the Ehresmann connection, and his seminar on category theory.

Life
Ehresmann was born in Strasbourg to a family which spoke the Alsatian language; his father was a gardener. He attended school in Strasbourg, then in 1924 went to university at the École Normale Supérieure in Paris. On graduating in 1927 he did one year of military service, and taught at a French school at Rabat in Morocco. He studied further at Göttingen during the years 1930-31, and at Princeton in 1932-34. He completed his PhD thesis entitled Sur la topologie de certains espaces homogènes (On the topology of certain homogeneous spaces) at ENS in 1934 under the supervision of Élie Cartan, and became a researcher with CNRS. From 1935 to 1937 he contributed to the seminar of Gaston Julia, which was a forerunner of the Bourbaki seminar.

Ehresmann was a lecturer at the French University of Strasbourg in 1939 when the German occupation of France irrupted, and the whole faculty was evacuated to Clermont-Ferrand. When Germany withdrew in 1945, he returned to Strasbourg. From 1955 he was Professor of Topology in Paris. His post was initially at the Sorbonne, but after the reorganization of Parisian universities in 1969 he moved to the University of Paris VII, Denis Diderot. He also held visiting chairs in Yale, Princeton, Brazil (São Paulo, Rio de Janeiro), Buenos Aires, Mexico, Montreal, and Bombay (Tata Institute); and was awarded an Honorary Doctorate by the University of Bologna. He was President of the Société Mathématique de France in 1965. He retired in 1975.

After retirement and until 1978 he gave lectures at the University of Picardy at Amiens, to which he moved because his second wife, Andrée Charles-Ehresmann, was a professor of mathematics there. He died at Amiens in 1979.

Mathematical work
Ehresmann first investigated the topology and homology of manifolds associated with classical Lie groups, such as Grassmann manifolds and other homogeneous spaces. He developed the concept of fiber bundle, building on work by Herbert Seifert and Hassler Whitney. Norman Steenrod was working in the same direction in the USA, but Ehresmann was particularly interested in differentiable (smooth) fiber bundles, and in differential-geometric aspects of these. He was a pioneer of differential topology. By 1957, having become a leading proponent of categorical methods, he founded the mathematical journal Cahiers de Topologie et Géométrie Différentielle Catégoriques.

Jean Dieudonné described Ehresmann's personality as "... distinguished by forthrightness, simplicity, and total absence of conceit or careerism. As a teacher he was outstanding, not so much for the brilliance of his lectures as for the inspiration and tireless guidance he generously gave to his research students ... "

He had 76 PhD students, including Georges Reeb, Wu Wenjun (吴文俊), André Haefliger, Valentin Poénaru, and Daniel Tanré. His first student was Jacques Feldbau.

His published works include the books 1965 Catégories et structures (Dunod, Paris, 1965) and Algèbre (1969). His collected works, edited by his wife, appeared in seven volumes in 1980-1983 (four volumes published by Imprimerie Evrard, Amiens, and the rest in the journal Cahiers de Topologie et de Géométrie Différentielle which he had founded).