After the war, he completed his studies and in 1948 he defended his PhD thesis, entitled Propriétés topologiques des variétés feuilletées [Topological properties of foliated manifolds] and supervised by Charles Ehresmann.[2]
There, in 1965 he created with Jean Leray and Pierre Lelong the series of meeting Rencontres entre Mathématiciens et Physiciens Théoriciens. in 1966 Reeb and Jean Frenkel founded the Institute de Recherche mathématique Avancée, the first university laboratory associated to the Centre National de la Recherche Scientifique, which he directed between 1967 and 1972.[4]
Reeb was the founder of the topological theory of foliations, a geometric structure on smooth manifolds which partition them in smaller pieces. In particular, he described what is now called the Reeb foliation, a foliation of the 3-sphere, whose leaves are all diffeomorphic to , except one, which is a 2-torus.[6]
His works on foliations had also applications in Morse theory. In particular, the Reeb sphere theorem says that a compact manifold with a function with exactly two critical points is homeomorphic to the sphere. In turn, in 1956 this was used to prove that the Milnor spheres, although not diffeomorphic, are homeomorphic to the sphere .[7]
^"Some historical facts". u-strasbg.fr. Institute for Advanced Mathematical Research, University of Strasbourg. Archived from the original on 2013-10-02. Retrieved 2020-02-10.
^Nelson, Edward (1995). "Ramified recursion and intuitionism"(PDF). Presented to Colloque Trajectorien: à la mémoire de Georges Reeb et Jean-Louis Callot. Strasbourg/Obernai.
