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Henri Cartan in 1968
Henri Paul Cartan
(1904-07-08)8 July 1904
|Died||13 August 2008(2008-08-13) (aged 104)
|Alma mater||École Normale Supérieure|
|Known for||Cartan's theorems A and B
Several complex variables
|Awards||Wolf Prize (1980)|
|Institutions||University of Paris|
|Doctoral advisor||Paul Montel|
|Doctoral students||Jean-Paul Benzécri
Henri Paul Cartan (French: [kaʁtɑ̃]; 8 July 1904 – 13 August 2008) was a French mathematician who made substantial contributions to algebraic topology. He was the son of the French mathematician Élie Cartan and the brother of composer Jean Cartan.
Cartan studied at the Lycée Hoche in Versailles, then at the École Normale Supérieure in Paris, receiving his doctorate in mathematics. He taught at the University of Strasbourg from November 1931 until the outbreak of the Second World War, after which he held academic positions at a number of other French universities, spending the bulk of his working life in Paris.
Cartan is known for work in algebraic topology, in particular on cohomology operations, the method of "killing homotopy groups", and group cohomology. His seminar in Paris in the years after 1945 covered ground on several complex variables, sheaf theory, spectral sequences and homological algebra, in a way that deeply influenced Jean-Pierre Serre, Armand Borel, Alexander Grothendieck and Frank Adams, amongst others of the leading lights of the younger generation. The number of his official students was small, but includes Joséphine Guidy Wandja (the first African woman to gain a PhD in mathematics), Adrien Douady, Roger Godement, Max Karoubi, Jean-Louis Koszul, Jean-Pierre Serre and René Thom.
Cartan also was a founding member of the Bourbaki group and one of its most active participants. His book with Samuel Eilenberg Homological Algebra  was an important text, treating the subject with a moderate level of abstraction with the help of category theory.
Cartan used his influence to help obtain the release of some dissident mathematicians, including Leonid Plyushch and Jose Luis Massera. For his humanitarian efforts, he received the Pagels Award from the New York Academy of Sciences.
The Cartan model in algebra is named after Cartan.
Honours and awards
Cartan received numerous honours and awards including the Wolf Prize in 1980. He was an Invited Speaker at the ICM in 1932 in Zürich and a Plenary Speaker at the ICM in 1950 in Cambridge, Massachusetts and in 1958 in Edinburgh. From 1974 until his death he had been a member of the French Academy of Sciences. He was a foreign member of the Finnish Academy of Science and Letters, Royal Danish Academy of Sciences and Letters, Royal Society of London, Russian Academy of Sciences, Royal Swedish Academy of Sciences, United States National Academy of Sciences, Polish Academy of Sciences and other academies and societies.
- Sur les systèmes de fonctions holomorphes à variétés linéaires lacunaires et leurs applications, thèse, 1928
- Sur les groupes de transformations analytiques, 1935.
- Sur les classes de fonctions définies par des inégalités portant sur leurs dérivées successives, 1940.
- Espaces fibrés et homotopie, 1949-1950.
- Cohomologie des groupes, suite spectrale, faisceaux, 1950-1951.
- Algèbres d'Eilenberg - Mac Lane et homotopie, 1954-1955.
- Fonctions automorphes, 1957-1958.
- Quelques questions de topologie, 1958.
- Homological Algebra (with S. Eilenberg), Princeton Univ Press, 1956 ISBN 978-0-69104991-5
- Séminaires de l'École normale supérieure (called "Séminaires Cartan"), Secr. Math. IHP, 1948-1964; New York, W.A.Benjamin ed., 1967.
- Théorie élémentaire des fonctions analytiques, Paris, Hermann, 1961 (translated into English, German, Japanese, Spanish and Russian).
- Calcul différentiel, Paris, Hermann, 1967 (translated into English, Spanish and Russian).
- Formes différentielles, Paris, Hermann, 1967 (translated into English, Spanish and Russian).
- Differential Forms, Dover 2006
- Œuvres — Collected Works, 3 vols., ed. Reinhold Remmert & Jean-Pierre Serre, Springer Verlag, Heidelberg, 1967.
- Relations d'ordre en théorie des permutations des ensembles finis, Neuchâtel, 1973.
- Théorie élémentaire des fonctions analytiques d'une ou plusieurs variables complexes, Paris, Hermann, 1975.
- Cours de calcul différentiel, Paris, Hermann, 1977.
- Correspondance entre Henri Cartan et André Weil, Paris, SMF, 2011.
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