Henri Cartan
Encyclopedia
Henri Paul Cartan was a French
mathematician
with substantial contributions in algebraic topology
. He was the son of the French mathematician Élie Cartan
.
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 operation
s, the method of "killing homotopy group
s", and group cohomology
. His seminar in Paris in the years after 1945 covered ground on several complex variables
, sheaf theory, spectral sequence
s 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 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 (1956) was an important text, treating the subject with a moderate level of abstraction and 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.
Cartan died on 13 August 2008 at the age of 104. His funeral took place the following Wednesday on 20 August in Die, Drome
.
. 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.
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
with substantial contributions in algebraic topology
Algebraic topology
Algebraic topology is a branch of mathematics which uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence.Although algebraic topology...
. He was the son of the French mathematician Élie Cartan
Élie Cartan
Élie Joseph Cartan was an influential French mathematician, who did fundamental work in the theory of Lie groups and their geometric applications...
.
Life
Cartan studied at the Lycée HocheLycée Hoche
The Lycée Hoche is a public secondary school located in Versailles, not very far away from the famous Palace of Versailles. Formerly, it had been a nunnery founded by French queen Maria Leszczyńska. However, after the French Revolution, it became a school in 1803...
in Versailles, then at the École Normale Supérieure
École Normale Supérieure
The École normale supérieure is one of the most prestigious French grandes écoles...
in Paris, receiving his doctorate in mathematics. He taught at the University of Strasbourg
University of Strasbourg
The University of Strasbourg in Strasbourg, Alsace, France, is the largest university in France, with about 43,000 students and over 4,000 researchers....
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
Paris
Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...
.
Cartan is known for work in algebraic topology
Algebraic topology
Algebraic topology is a branch of mathematics which uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence.Although algebraic topology...
, in particular on cohomology operation
Cohomology operation
In mathematics, the cohomology operation concept became central to algebraic topology, particularly homotopy theory, from the 1950s onwards, in the shape of the simple definition that if F is a functor defining a cohomology theory, then a cohomology operation should be a natural transformation from...
s, the method of "killing homotopy group
Homotopy group
In mathematics, homotopy groups are used in algebraic topology to classify topological spaces. The first and simplest homotopy group is the fundamental group, which records information about loops in a space...
s", and group cohomology
Group cohomology
In abstract algebra, homological algebra, algebraic topology and algebraic number theory, as well as in applications to group theory proper, group cohomology is a way to study groups using a sequence of functors H n. The study of fixed points of groups acting on modules and quotient modules...
. His seminar in Paris in the years after 1945 covered ground on several complex variables
Several complex variables
The theory of functions of several complex variables is the branch of mathematics dealing with functionson the space Cn of n-tuples of complex numbers...
, sheaf theory, spectral sequence
Spectral sequence
In homological algebra and algebraic topology, a spectral sequence is a means of computing homology groups by taking successive approximations...
s and homological algebra
Homological algebra
Homological algebra is the branch of mathematics which studies homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology and abstract algebra at the end of the 19th century, chiefly by Henri Poincaré and...
, in a way that deeply influenced Jean-Pierre Serre
Jean-Pierre Serre
Jean-Pierre Serre is a French mathematician. He has made contributions in the fields of algebraic geometry, number theory, and topology.-Early years:...
, Armand Borel
Armand Borel
Armand Borel was a Swiss mathematician, born in La Chaux-de-Fonds, and was a permanent professor at the Institute for Advanced Study in Princeton, New Jersey, United States from 1957 to 1993...
, Alexander Grothendieck
Alexander Grothendieck
Alexander Grothendieck is a mathematician and the central figure behind the creation of the modern theory of algebraic geometry. His research program vastly extended the scope of the field, incorporating major elements of commutative algebra, homological algebra, sheaf theory, and category theory...
and Frank Adams
Frank Adams
John Frank Adams FRS was a British mathematician, one of the founders of homotopy theory.-Life:He was born in Woolwich, a suburb in south-east London. He began research as a student of Abram Besicovitch, but soon switched to algebraic topology. He received his Ph.D. from the University of...
, amongst others of the leading lights of the younger generation. The number of his official students was small, but includes Adrien Douady
Adrien Douady
Adrien Douady was a French mathematician.He was a student of Henri Cartan at the Ecole Normale Supérieure, and initially worked in homological algebra. His thesis concerned deformations of complex analytic spaces...
, Roger Godement
Roger Godement
Roger Godement is a French mathematician, known for his work in functional analysis, and also his expository books.He started as a student at the École normale supérieure in 1940, where he became a student of Henri Cartan...
, Max Karoubi, Jean-Louis Koszul
Jean-Louis Koszul
Jean-Louis Koszul is a mathematician best known for studying geometry and discovering the Koszul complex.He was educated at the Lycée Fustel-de-Coulanges in Strasbourg before studying at the Faculty of Science in Strasbourg and the Faculty of Science in Paris...
, Jean-Pierre Serre
Jean-Pierre Serre
Jean-Pierre Serre is a French mathematician. He has made contributions in the fields of algebraic geometry, number theory, and topology.-Early years:...
and René Thom
René Thom
René Frédéric Thom was a French mathematician. He made his reputation as a topologist, moving on to aspects of what would be called singularity theory; he became world-famous among the wider academic community and the educated general public for one aspect of this latter interest, his work as...
.
Cartan also was a founding member of the Bourbaki
Nicolas Bourbaki
Nicolas Bourbaki is the collective pseudonym under which a group of 20th-century mathematicians wrote a series of books presenting an exposition of modern advanced mathematics, beginning in 1935. With the goal of founding all of mathematics on set theory, the group strove for rigour and generality...
group and one of its most active participants. His book with Samuel Eilenberg
Samuel Eilenberg
Samuel Eilenberg was a Polish and American mathematician of Jewish descent. He was born in Warsaw, Russian Empire and died in New York City, USA, where he had spent much of his career as a professor at Columbia University.He earned his Ph.D. from University of Warsaw in 1936. His thesis advisor...
Homological Algebra (1956) was an important text, treating the subject with a moderate level of abstraction and category theory
Category theory
Category theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows , where these collections satisfy certain basic conditions...
.
Cartan used his influence to help obtain the release of some dissident
Dissident
A dissident, broadly defined, is a person who actively challenges an established doctrine, policy, or institution. When dissidents unite for a common cause they often effect a dissident movement....
mathematicians, including Leonid Plyushch
Leonid Plyushch
Leonid Plyushch is a mathematician and Soviet dissident.- Early life and career :Leonid Plyushch was born into a Ukrainian working-class family in 1939 in Naryn, Kirghizia. His father worked as railway foreman, and was killed at the front 1941...
and Jose Luis Massera
José Luis Massera
José Luis Massera was an Uruguayan mathematician who researched the stability of differential equations....
. For his humanitarian efforts he received the Pagels Award from the New York Academy of Sciences
New York Academy of Sciences
The New York Academy of Sciences is the third oldest scientific society in the United States. An independent, non-profit organization with more than members in 140 countries, the Academy’s mission is to advance understanding of science and technology...
.
The Cartan model
Cartan model
In mathematics, the Cartan model is a differential graded algebra that computes the equivariant cohomology of a space.-References:* Stefan Cordes, Gregory Moore, Sanjaye Ramgoolam, Lectures on 2D Yang-Mills Theory, Equivariant Cohomology and Topological Field Theories, , 1994....
in algebra is named after Cartan.
Cartan died on 13 August 2008 at the age of 104. His funeral took place the following Wednesday on 20 August in Die, Drome
Die, Drôme
Die is a commune, former episcopal see, and sub-prefecture of the Drôme department in southeastern France.Die is best known for the Clairette de Die, a sparkling wine. It was a county in the High Middle Ages.-Population:-External links:*...
.
Honours and awards
Cartan received numerous honours and awards including the Wolf Prize in 1980. From 1974 until his death he had been a member of the French Academy of SciencesFrench Academy of Sciences
The French Academy of Sciences is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research...
. He was a foreign member of the Finnish Academy of Science and Letters
Finnish Academy of Science and Letters
The Finnish Academy of Science and Letters is a Finnish learned society. It was founded in 1908 as a Finnish-language counterpart of the Swedish-language Finnish Society of Sciences and Letters, which had existed since 1838.- Members :The academy has a total of 328 seats for Finnish members...
, Royal Danish Academy of Sciences and Letters
Royal Danish Academy of Sciences and Letters
Royal Danish Academy of Sciences and Letters is a Danish non-governmental science Academy, founded 13 November 1742 by permission of the King Christian VI, as a historical Collegium Antiquitatum...
, Royal Society of London, Russian Academy of Sciences
Russian Academy of Sciences
The Russian Academy of Sciences consists of the national academy of Russia and a network of scientific research institutes from across the Russian Federation as well as auxiliary scientific and social units like libraries, publishers and hospitals....
, Royal Swedish Academy of Sciences
Royal Swedish Academy of Sciences
The Royal Swedish Academy of Sciences or Kungliga Vetenskapsakademien is one of the Royal Academies of Sweden. The Academy is an independent, non-governmental scientific organization which acts to promote the sciences, primarily the natural sciences and mathematics.The Academy was founded on 2...
, United States National Academy of Sciences
United States National Academy of Sciences
The National Academy of Sciences is a corporation in the United States whose members serve pro bono as "advisers to the nation on science, engineering, and medicine." As a national academy, new members of the organization are elected annually by current members, based on their distinguished and...
, Polish Academy of Sciences
Polish Academy of Sciences
The Polish Academy of Sciences, headquartered in Warsaw, is one of two Polish institutions having the nature of an academy of sciences.-History:...
and other academies and societies.
External links
- Henri Cartan at l'Académie des Sciences
- Biographical sketch and bibliography by the Société Mathématique de FranceSociété Mathématique de FranceThe Société Mathématique de France is the main professional society of French mathematicians.The society was founded in 1872 by Émile Lemoine and is one of the oldest mathematical societies in existence...
on the occasion of Cartan's 100th birthday. (translations of above two articles from the SMF Gazette)