# Charles Ehresmann

### Quick Info

Strasbourg, Alsace (now France)

Amiens France

**Charles Ehresmann**was a French mathematician who worked in differential topology and category theory.

### Biography

**Charles Ehresmann**came from a poor family in Alsace. His father was a gardener and the family spoke Alsatian which is related to the Germanic languages. Alsace, which was originally French, had came under German rule in 1871 but by 1902 had effective self-government. After 1911 it had its own constitution and progress was made toward Germanisation in the region. Certainly Charles began his schooling entirely in German up to the end of World War I in 1918. He attended the Lycée Kléber in Strasbourg but, after 1919 Alsace was returned to France and French language schools were set up. This met with resistance from the German speaking population but their attempts at autonomy within the French Republic were unsuccessful. Charles, however, was from that time on taught in French.

In 1924 Ehresmann entered the École Normale Supérieure in Paris. He graduated in 1927, spent a year doing military service, then taught mathematics at the French speaking Lycée in Rabat, the national capital of Morocco. After spending the years 1928-29 in Rabat, Ehresmann continued his education going to Göttingen to undertake research. During his time in Göttingen in the years 1930 and 1931 it was the leading centre for mathematical research in the world although, of course, shortly after this the rise to power of the Nazis would change the mathematical world significantly.

From 1932 to 1934 Ehresmann studied at Princeton in the United States. Having left the leading centre of Göttingen, he had gone to the place which in many ways would replace it as the leading mathematical centre as the Jewish mathematicians left Germany after the Nazis passed their anti-Jewish legislation in 1933.

Ehresmann's doctorate was awarded by Paris in 1934. In his doctoral dissertation, and during the time from 1934 to 1939 when he was carrying out research in the Centre Nationale de la Recherche Scientifique, he studied topological properties of differential manifolds. In particular he described [1]:-

... the homology of classical types of homogeneous manifolds, such as Grassmannians, flag manifolds, Stiefel manifolds, and classical groups.He became a lecturer in the University of Strasbourg in 1939 but shortly after this he was back in the middle of the France/Germany conflict of his youth but this time on a quite different scale as the Germans invaded Alsace in 1940. During the German occupation of World War II, the University of Strasbourg's faculties were moved to Clermont Ferrand University in central France, then back to Strasbourg in 1945. Ehresmann followed the moves of the university then, in 1955, a chair of topology was specially created for him in the University of Paris. He held this chair until he retired in 1975.

Although he was 70 years old when he retired, Ehresmann did not give up lecturing for at this time he moved to Amiens, where his second wife was a professor of mathematics, and he taught there.

Ehresmann was one of the creators of differential topology. Beginning in 1941, Ehresmann made major contributions toward establishing the current view of fibre spaces, manifolds, foliations and jets. His work in the creation and development of fibre spaces followed on from the study of a special case made earlier by Seifert and Whitney.

After 1957 Ehresmann became a leader in category theory and he worked in this area for 20 years. His principal achievements in this area concern local categories and structures defined by atlases, and germs of categories. The article [3] contains a list of 139 articles written by Ehresmann during his productive career as well as listing several volumes which he edited.

Between 1980 and 1983 Andrée Charles Ehresmann, his wife, edited his complete works. These appeared in seven volumes:

*Charles Ehresmann: Oeuvres complètes et commentées*Ⓣ as supplements to the Journal

*Cahiers de Topologie et Géometrie Différentielle Categoriques*which Charles Ehresmann created in 1957.

In [1] Dieudonné describes 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 ...

### References (show)

- J Dieudonne, Biography in
*Dictionary of Scientific Biography*(New York 1970-1990). See THIS LINK. - A C Ehresmann,
*Charles Ehresmann, Oeuvres complète et commentées*(Supplements to*Cahiers de Topologie et Géométrie Différentielle Categoriques*, 1980-83). - A C Ehresmann, Liste des publications de Charles Ehresmann,
*Cahiers Topologie Géom. Différentielle***20**(3) (1979), i-ii, 221-229. - A C Ehresmann, An introduction to the 3ième Colloque sur les Catégories, dédié à Charles Ehresmann, Third Colloquium on Categories, Amiens, 1980, Part I,
*Cahiers Topologie Géom. Différentielle***21**(4) (1980), 347-352. - S Mac Lane, The genesis of mathematical structures, as exemplified in the work of Charles Ehresmann, Third Colloquium on Categories Part I,
*Cahiers Topologie Géom. Différentielle***21**(4) (1980), 353-365.

### Additional Resources (show)

Other websites about Charles Ehresmann:

### Cross-references (show)

Written by J J O'Connor and E F Robertson

Last Update July 2000

Last Update July 2000