Georges Reeb

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Georges Reeb
Born	(1920-11-12)12 November 1920 Saverne, France
Died	6 November 1993(1993-11-06) (aged 72) Strasbourg, France
Nationality	French
Alma mater	University of Strasbourg
Scientific career
Fields	Mathematics
Institutions	University of Strasbourg
Doctoral advisor	Charles Ehresmann

Georges Henri Reeb (12 November 1920 – 6 November 1993) 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.^[1] He was married with Gertrude Siefert. Saverne is located about 40 km (25 mi) from Strasbourg.^[1]

In 1948 he received his PhD from University of Strasbourg (that had been evacuated during the war to Clermont-Ferrand) with the dissertation Propriétés topologiques des variétés feuilletées. His adviser was Charles Ehresmann.^[1]

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 (Rencontres entre Mathématiciens et Physiciens Théoriciens).

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 in 1966.^[2]

Reeb was the founder of the topological theory of foliations (Feuilletages, Blätterungen), 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 (compact!) 2-torus.^[3]

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 graph
• Reeb vector field
• Reeb stability theorem

Reeb received an honorary doctorate from the Albert-Ludwigs-Universität Freiburg and from the Université de Neuchâtel.

Quotes[]

• The naïve integers don't fill up ${\displaystyle \mathbb {N} }$.^[4]

Personal life and demise[]

Reeb died in Strasbourg, France.^[1] He was 72 years old.

Selected works[]

Books[]

• with Wu Wen-Tsün: Sur les espaces fibrés et les variétés feuilletées, 1952^[5]
• with A. Fuchs: Statistiques commentées, 1967
• with J. Klein: Formules commentées de mathématiques: Programme P.C., 1971
• Feuilletages: résultats anciens et nouveaux (Painlevé, Hector et Martinet), 1974

Articles[]

• "Sur les points singuliers d'une forme de Pfaff complètement intégrable ou d'une fonction numérique". C. R. Acad. Sci. Paris. 222: 847–849. 1946.
• "Variétés feuilletées, feuilles voisines". C. R. Acad. Sci. Paris. 224: 1613–1614. 1947.
• "Sur certaines propriétés topologiques des variétés feuilletées". Actualités Sci. Ind., Publ. Inst. Math. Univ. Strasbourg. Paris: Hermann & Cie. 11 (1183): 5–89, 155–156. 1952.
• with André Haefliger: "Variétés (non séparées) à une dimension et structures feuilletées du plan". Enseignement Math. 2 (3): 107–125. 1957.

See also[]

• Contact geometry
• Séminaire Nicolas Bourbaki
• Séminaire Nicolas Bourbaki (1950–1959)

References[]

External links[]

Wikimedia Commons has media related to Georges Henri Reeb (mathematician).

• RAMIFIED RECURSION AND INTUITIONISM in memory of Georges Reeb