Charles Ehresmann


Charles Ehresmann was a German-born 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 differential geometry of smooth fiber bundles, notably the Ehresmann connection, the concept of jets of a smooth map, 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 the University of Göttingen during the years 1930–31, and at Princeton University in 1932–34. He completed his Ph.D. thesis entitled Sur la topologie de certains espaces homogènes at ENS in 1934 under the supervision of Élie Cartan, and became a researcher with the Centre national de la recherche scientifique. 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 Paris Diderot University. He also held visiting chairs at Yale University, Princeton University, in Brazil, Buenos Aires, Mexico City, Montreal, and the Tata Institute of Fundamental Research in Bombay; 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 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, André Haefliger, Valentin Poénaru, and Daniel Tanré. His first student was Jacques Feldbau.
His publications include the books 1965 Catégories et structures and Algèbre. His collected works, edited by his wife, appeared in seven volumes in 1980–1983.