Jean Cerf (born in 1928) is a French mathematician, specializing in topology.

Education and career

Jean Cerf was born in Strasbourg, France, in 1928. He studied at the

École Normale Supérieure École may refer to: * an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing in région Île-de-France * École, Savoi ...

, graduating in sciences in 1947. After passing his ''

agrégation In France, the ''agrégation'' () is a competitive examination for civil service in the French public education system. Candidates for the examination, or ''agrégatifs'', become ''agrégés'' once they are admitted to the position of ''professe ...

'' in mathematics in 1950, he obtained a doctorate with thesis supervised by Henri Cartan. Cerf became a ''

maître de conférences ''Maître'' (spelled ''Maitre'' according to post-1990 spelling rules) is a commonly used honorific for lawyers, judicial officers and notaries in France, Belgium, Switzerland and French-speaking parts of Canada. It is often written in its abbrev ...

'' at the

University of Lille The University of Lille (french: Université de Lille, abbreviated as ULille, UDL or univ-lille) is a French public research university based in Lille, Hauts-de-France. It has its origins in the University of Douai (1559), and resulted from the m ...

and was later appointed a professor at the

University of Paris XI Paris-Sud University (French: ''Université Paris-Sud''), also known as University of Paris — XI (or as Université d'Orsay before 1971), was a French research university distributed among several campuses in the southern suburbs of Paris, in ...

. He was also a director of research at

CNRS The French National Centre for Scientific Research (french: link=no, Centre national de la recherche scientifique, CNRS) is the French state research organisation and is the largest fundamental science agency in Europe. In 2016, it employed 31,637 ...

. Cerf's research deals with

differential topology In mathematics, differential topology is the field dealing with the topological properties and smooth properties of smooth manifolds. In this sense differential topology is distinct from the closely related field of differential geometry, which ...

cobordism In mathematics, cobordism is a fundamental equivalence relation on the class of compact manifolds of the same dimension, set up using the concept of the boundary (French '' bord'', giving ''cobordism'') of a manifold. Two manifolds of the same dim ...

, and

symplectic topology Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2-form. Symplectic geometry has its origins in the H ...

. In 1966 he was an Invited Speaker at the ICM in

Moscow Moscow ( , US chiefly ; rus, links=no, Москва, r=Moskva, p=mɐskˈva, a=Москва.ogg) is the capital and largest city of Russia. The city stands on the Moskva River in Central Russia, with a population estimated at 13.0 million ...

. In 1968 Cerf proved that every orientation-preserving

diffeomorphism In mathematics, a diffeomorphism is an isomorphism of smooth manifolds. It is an invertible function that maps one differentiable manifold to another such that both the function and its inverse are differentiable. Definition Given two m ...

S^3

is isotopic to the identity.J. Cerf, Sur les difféomorphismes de la sphère de dimension trois (Γ₄=0), Lecture Notes in Mathematics, No. 53. Springer-Verlag, Berlin-New York 1968. (See

Cerf theory In mathematics, at the junction of singularity theory and differential topology, Cerf theory is the study of families of smooth real-valued functions :f\colon M \to \R on a smooth manifold M, their generic singularities and the topology of the ...

.) In 1970 Cerf proved the pseudo-isotopy theory for simply connected manifolds. In 1970 he was awarded the ''prix Servant'', together with Bernard Malgrange and

André Néron André Néron (November 30, 1922, La Clayette, France – April 6, 1985, Paris, France) was a French mathematician at the Université de Poitiers who worked on elliptic curves and abelian varieties. He discovered the Néron minimal model of a ...

(for independent work). 1971 he was the president of the

Société Mathématique de France Lactalis is a French multinational dairy products corporation, owned by the Besnier family and based in Laval, Mayenne, France. The company's former name was Besnier SA. Lactalis is the largest dairy products group in the world, and is the sec ...

Selected publications

" Groupes d'automorphismes et groupes de difféomorphismes des variétés compactes de dimension 3."
Bull. Soc. Math. France 87 (1959): 319–329.
"Topologie de certains espaces de plongements."
Bull. Soc. Math. France 89, no. 196 (1961): 227–380.
"Théorèmes de fibration des espaces de plongements. Applications."
Séminaire Henri Cartan 15 (1962): 1–13.
"Travaux de Smale sur la structure des variétés."
Seminaire Bourbaki 7 (1962): 113–128. *"La nullité de Γ₄, généralisation du théorème de Schönflies pour S²." In Sur les difféomorphismes de la sphère de dimension trois (Γ4= O), pp. 1–10. Springer, Berlin, Heidelberg, 1968. *"La stratification naturelle des espaces de fonctions différentiables réelles et le théoreme de la pseudo-isotopie." Publications Mathématiques de l'Institut des Hautes Études Scientifiques 39, no. 1 (1970): 7–170.

References

{{DEFAULTSORT:Cerf, Jean 1928 births Living people 20th-century French mathematicians 21st-century French mathematicians École Normale Supérieure alumni Academic staff of the University of Paris Topologists Academic staff of the Lille University of Science and Technology