# Charles Ehresmann

**Charles Ehresmann** (19 April 1905 – 22 September 1979) 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, [1] and his seminar on category theory.

Charles Ehresmann | |
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Charles Ehresmann (right) at the topology conference 1949 in Oberwolfach, together with Paul Vincensini (middle) and Georges Reeb (left) | |

Born | |

Died | 22 September 1979 74) | (aged

Alma mater | École Normale Supérieure |

Known for | Ehresmann's fibration theorem Ehresmann connection |

Scientific career | |

Fields | Mathematics |

Institutions | University of Strasbourg Paris Diderot University |

Doctoral advisor | Élie Cartan |

Doctoral students | Jacques Feldbau Georges Reeb Wu Wen-Tsün André Haefliger Valentin Poénaru Nguyen Dinh Ngoc |

## 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 (ENS) 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* (On the topology of certain homogeneous spaces) at ENS in 1934 under the supervision of Élie Cartan, and became a researcher with the Centre national de la recherche scientifique (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 Paris Diderot University (Paris 7). He also held visiting chairs at Yale University, Princeton University, in Brazil (São Paulo, Rio de Janeiro), 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 (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.[2]

His publications 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 Géométrie Différentielle Catégoriques* which he had founded).

## See also

## Notes

- See the entry "Jet bundle" for more details.
- According to Michèle Audin.

## References

- International Conference "Charles Ehresmann: 100 ans" Université de Picardie Jules Verne à Amiens, 7-8-9 October 2005. http://pagesperso-orange.fr/vbm-ehr/ChEh/indexAng.htm
- 'The mathematical legacy of Charles Ehresmann', Proceedings of the 7th Conference on the Geometry and Topology of Manifolds: The Mathematical Legacy of Charles Ehresmann, Będlewo (Poland), 8.05.2005–15.05.2005, Edited by J. Kubarski, J. Pradines, T. Rybicki, R. Wolak, Banach Center Publications, vol. 76, Institute of Mathematics of the Polish Academy of Sciences, Warsaw, 2007. https://www.impan.pl/pl/wydawnictwa/banach-center-publications/all/76

## External links

- O'Connor, John J.; Robertson, Edmund F., "Charles Ehresmann",
*MacTutor History of Mathematics archive*, University of St Andrews. - Charles Ehresmann at the Mathematics Genealogy Project
- Michèle Audin. "Publier sous l'Occupation. Autour du cas de Jacques Feldbau et de l'Académie des Sciences" (PDF).