Georges Reeb


Georges Henri Reeb was a French mathematician. He worked in differential topology, differential geometry, differential equations, topological dynamical systems theory and non-standard analysis.

Early life and education

Reeb was born in Saverne, Bas-Rhin, Alsace, to Theobald Reeb and Caroline Engel. He had a sister, Gertrude. Saverne is located about from Strasbourg.
In 1943 he received his PhD from University of Strasbourg with the dissertation Propriétés topologiques des variétés feuilletées. His adviser was Charles Ehresmann.

Career

In 1954, he was at the Institute for Advanced Study.
In 1965 Reeb, Jean Leray and Pierre Lelong founded a series of encounters between theoretical physicists and mathematicians in Strasbourg.
He was a professor at Université Joseph Fourier in Grenoble and Université Louis Pasteur in Strasbourg where he directed the Institute for Advanced Mathematical Research at University of Strasbourg between 1967 and 1972, which he founded with Jean Frenkel in 1966.
Reeb was the founder of the topological theory of foliations, manifolds with a special local product structure. He invented what is now called the Reeb foliation, a foliation of the 3-sphere, all the leaves of which are diffeomorphic to R2, except one, which is a 2-torus.
Reeb sphere theorem says that a compact manifold with a function with exactly two critical points is homeomorphic to the sphere. This is used to prove that the Milnor spheres, although not diffeomorphic, are homeomorphic to the sphere S7, a result that came in 1956.
Other terms named for Reeb are:
Reeb received an honorary doctorate from the :de:Albert-Ludwigs-Universität Freiburg|Albert-Ludwigs-Universität Freiburg and from the Université de Neuchâtel.

Quotes

Reeb died in Strasbourg, France. He was 72 years old.

Selected works

Books