Jacques Feldbau
Jacques Feldbau | |
---|---|
University of Straßburg | |
Known for | Feldbau's theorem: a fiber bundle over a simplex is trivializable |
Scientific career | |
Fields | Mathematics |
Doctoral advisor | Charles Ehresmann |
Jacques Feldbau was a French mathematician, born on 22 October 1914 in
He is known as one of the founders of the theory of fiber bundles. He is the one who first proved that a fiber bundle over a simplex is trivializable and who used this to classify bundles over spheres.[1]
In a paper, written together with Ehresmann, he introduced the notion of an associated bundle and proved results known today as the exact homotopy sequence of a fibration.[2]
Biography
Childhood and education
Described by Michèle Audin as "a handsome young man with a very friendly and likeable personality"[citation needed] he demonstrated an early interest in mathematics, whilst also being enthusiastic about music and sport. He studied at the Lycée Fustel de Coulanges in Strasbourg, receiving his high school diploma in 1932, and then he started preparatory classes at Lycée Kléber. He applied for the École normale supérieure but refused to present himself on Saturday (the Jewish sabbath), and so was not allowed to continue. He enrolled at the University of Strasbourg in 1934, where he was librarian of the Institute of Mathematics in 1935. He joined the CNRS and began preparing a PhD under the direction of Charles Ehresmann in 1939. He was also a pianist and swimmer. becoming a university butterfly-stroke champion in 1939. By the age 30, Feldbau was participating in a "defence group against anti-Semitism."
World War II
Mobilized in 1939, he became a flying officer in the French Air Force. Demobilized after the armistice of 22 June 1940, he was appointed associate professor at the School of Chateauroux, but was forbidden to teach by the laws of exclusions of 3 October 1940 on the status of Jews, promulgated by the
Closer to the war, a very gifted student, Jacques Feldbau, asked me to suggest a topic in topology. I consulted Ehresmann, who was far better versed in the field than I. Following his advice, I suggested to Feldbau that he study the notion of fiber bundles, which was still quite young. Despite his somewhat clumsy methods (hardly surprising in a beginner) he came up with some interesting results...
, The Apprenticeship of a Mathematician, p. 112
Arrest and deportation
On the night of 24 to 25 June 1943 the "roundup of Gallia" took place whereby 38 Strasbourg university students were arrested in the Gallia university foyer in retaliation for three attacks against the Germans, following the execution on 24 June of two members of the
His remains were repatriated in 1957 by his sister, and he was reinterred in Cronenbourg.
His mathematical work
At the instigation of Charles Ehresmann he conducted crucial work in algebraic topology and specifically on fiber spaces. Amongst its key findings, we note the following fundamental theorem: "a fiber space of a simplex is trivializable "and its corollary, "to give a bundle on a sphere is equivalent to giving a mapping from in the group of automorphisms of the fiber." These results are so obvious now among the specialists in algebraic topology that their origin is somewhat forgotten, writes André Weil, in the comments of his collected works. A note to the Proceedings of the Academy of Sciences, co-authored with Charles Ehresmann, outlines what was later called the homotopy exact sequence of fiber bundles.
The posthumous papers of Feldbau, published by Ehresmann in 1958, also include work on homotopy groups of higher order, later recovered, and overtaken by J. H. C. Whitehead, with whom he and Ehresmann were competing. His difficult working conditions and his tragic fate have overshadowed his contributions to mathematics, but his contributions are recognized by recent work on the history of the topology.[3][4]
See also
Notes
- ^ J. Feldbau (1939). "Sur la classification des espaces fibrés". C. R. Acad. Sci. Paris. 208: 1621–1623.
- ^ C. Ehresmann and J. Feldbau (1941). "Sur les propriétés d'homotopie des espaces fibrés". C. R. Acad. Sci. Paris. 212: 945–948.
- ISBN 0-8176-3388-X.
- ^ M. Zisman, Fibre bundles, fibre maps, in Ioan James (ed.); History of Topology, Amsterdam, North Holland 1999, pp. 605–629.