Georges Reeb

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.

Georges Reeb
Born(1920-11-12)12 November 1920
Saverne, France
Died6 November 1993(1993-11-06) (aged 72)
Strasbourg, France
NationalityFrench
Alma materUniversity of Strasbourg
Scientific career
FieldsMathematics
InstitutionsUniversity of Strasbourg
Doctoral advisorCharles Ehresmann

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

Quotes
  • The naïve integers don't fill up .[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

References
  1. "Georges Reeb (1920 - 1993)". MacTutor History of Mathematics archive. University of St Andrews. Retrieved 2020-02-10 – via st-andrews.ac.uk.
  2. "Some historical facts". u-strasbg.fr. Institute for Advanced Mathematical Research, University of Strasbourg. Retrieved 2020-02-10.
  3. "Differential Geometry" (PDF). Notices of the AMS. Strasbourg: American Mathematical Society (published online 2008). 1953. Retrieved 2020-02-10 – via AMS.org.
  4. Nonstandard Analysis in Practice, p. 4, at Google Books. Edited by Francine Diener, Marc Diener.
  5. Chern, Shiing-Shen (1953). "Review: Sur les espaces fibrés et les variétés feuilletées by W. T. Wu and G. Reeb". Bulletin of the American Mathematical Society. 59: 258–263. doi:10.1090/S0002-9904-1953-09700-2.
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