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 introduction of the concepts of Ehresmann connection and of jet bundles, and for his seminar on category theory.
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.[3]
From 1955 he was Professor of Topology at Sorbonne, and after the reorganization of Parisian universities in 1969 he moved to Paris Diderot University (Paris 7).
After his retirement in 1975 and until 1978 he gave lectures at the University of Picardy at Amiens, where he moved because his second wife, Andrée Charles-Ehresmann, was a professor of mathematics there. He died at Amiens in 1979.[1][2]
Mathematical workedit
In the first part of his career Ehresmann introduced many new mathematical objects in differential geometry and topology, which gave rise to entire new fields, often developed later by his students.[8][9][2]
Since the 1960s, Ehresmann's research interests moved to category theory, where he introduced the concepts of sketch and of strict 2-category.[28][29]
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 in 1957).[30] His publications include also the books Catégories et structures (Dunod, Paris, 1965) and Algèbre (1969).
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 ... "[2]
^"Liste anciens présidents | Société Mathématique de France". smf.emath.fr. Retrieved 18 February 2022.
^"Charles Ehresmann". serge.mehl.free.fr (in French). Retrieved 18 February 2022.
^"Lauree Honoris Causa – Archivio Storico". archiviostorico.unibo.it (in Italian). Retrieved 26 February 2022.
^"CTHS – EHRESMANN Charles". cths.fr. Retrieved 18 February 2022.
^Libermann, Paulette (2007). "Charles Ehresmann's concepts in differential geometry". Geometry and Topology of Manifolds. Banach Center Publications. 76. Będlewo, Poland: Institute of Mathematics Polish Academy of Sciences: 35–50. doi:10.4064/bc76-0-2.
^Ehresmann, Andrée C. (2007). "How Charles Ehresmann's vision of geometry developed with time". Geometry and Topology of Manifolds. Banach Center Publications. 76. Będlewo, Poland: Institute of Mathematics Polish Academy of Sciences: 29–34. doi:10.4064/bc76-0-1.
^Ehresmann, Charles (1934). "Sur la Topologie de Certains Espaces Homogenes". Annals of Mathematics. 35 (2): 396–443. doi:10.2307/1968440. ISSN 0003-486X. JSTOR 1968440.
^Ehresmann, Charles (1936). "Sur les espaces localement homogènes" [On locally homogeneous spaces]. Enseign. Math. (in French). 35: 317–333. JFM 62.1473.03.
^Marle, Charles-Michel (2007). "The works of Charles Ehresmann on connections: from Cartan connections to connections on fibre bundles". Geometry and Topology of Manifolds. Banach Center Publications. 76. Będlewo, Poland: Institute of Mathematics Polish Academy of Sciences: 65–86. arXiv:1401.8272. doi:10.4064/bc76-0-4. S2CID 43455645.
^Ehresmann, Charles (1947). "Sur les espaces fibrés différentiables" [On differentiable fibred bundles]. Comptes rendus de l'Académie des Sciences (in French). 224: 1611–1612. Zbl 0029.42001.
^Ehresmann, Charles (1949). "Sur la théorie des espaces fibres" [On the theory of fibred bundles]. Colloques Internat. Centre Nat. Rech. Sci. (Topologie Algebrique) (in French). 12: 3–15. Zbl 0039.39703.
^Ehresmann, Charles (1955). "Les prolongements d'un espace fibré différentiable" [The prolongations of a differentiable fibred bundle]. Comptes rendus de l'Académie des Sciences (in French). 240: 1755–1757.
^Seifert, Herbert (1933). "Topologie Dreidimensionaler Gefaserter Räume" [Topology of tridimensional fibred space]. Acta Mathematica (in German). 60: 147–238. doi:10.1007/BF02398271. ISSN 0001-5962. S2CID 122571694 – via Project Euclid.
^Whitney, Hassler (1 July 1935). "Sphere-Spaces". Proceedings of the National Academy of Sciences of the United States of America. 21 (7): 464–468. Bibcode:1935PNAS...21..464W. doi:10.1073/pnas.21.7.464. ISSN 0027-8424. PMC1076627. PMID 16588001.
^Ehresmann, Charles (1952). "Sur les variétés presques complexes" [On almost complex manifolds]. Proc. Internat. Congr. Math. (in French). 2: 412–419. Zbl 0049.12904.
^Hopf, Heinz (1948). "Zur Topologie der komplexen Mannigfaltigkeiten" [On the topology of complex manifolds]. Studies and Essays Presented to R. Courant on His 60th Birthday (in German). New York: 167–185.
^Haefliger, André (2005). "Naissance des feuilletages, d'Ehresmann-Reeb à Novikov" [Birth of foliations, from Ehresmann-Reeb to Novikov]. Géométrie au XXe Siècle, 1930-2000: Histoire et Horizons (in French). Hermann: 257–272. CiteSeerX10.1.1.694.1226.
^Reeb, Georges (1952). "Sur certaines propriétés topologiques des variétés feuilletées" [On certain topological properties of foliated manifolds]. Actualités Scientifiques et Industrielles (in French). 1183. Paris: Hermann: 5–89, 155–156. MR 0055692.
^Pradines, Jean (2007). "In Ehresmann's footsteps: from group geometries to groupoid geometries". Geometry and Topology of Manifolds. Banach Center Publications. 76. Będlewo, Poland: Institute of Mathematics Polish Academy of Sciences: 87–157. arXiv:0711.1608. doi:10.4064/bc76-0-5. S2CID 17743849.
^Tulczyjew, Włodzimierz M. (2007). "Evolution of Eresmann's jet theory". Geometry and Topology of Manifolds. Banach Center Publications. 76. Będlewo, Poland: Institute of Mathematics Polish Academy of Sciences: 159–176. doi:10.4064/bc76-0-6. S2CID 17456748.
^Ehresmann, Charles (1959). "Catégories topologiques et categories différentiables" [Topological categories and differentiable categories] (PDF). Colloque de Géométrie différentielle globale (in French). CBRM, Bruxelles: 137–150.
^Ehresmann, Charles (1963). "Catégories structurées" [Structured categories]. Annales scientifiques de l'École Normale Supérieure (in French). 80 (4): 349–426. doi:10.24033/asens.1125.
^Ehresmann, Charles (1968). "Esquisses et types des structures algébriques" [Sketches and types of algebraic structures]. Bul. Inst. Politeh. Iaşi, N. Ser. (in French). 14 (18): 1–14. MR 0238918. Zbl 0196.03102.
^"Oeuvres de Charles Ehresmann". ehres.pagesperso-orange.fr. Retrieved 18 February 2022.
^Audin, Michèle (2009). "Publier sous l'Occupation. Autour du cas de Jacques Feldbau et de l'Académie des Sciences" [Publish under the Occupation. On the case of Jacques Feldbau and the Academy of Sciences]. Revue d'histoire des mathématiques (in French). 15 (1): 7–57.
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