Jacques Feldbau | |
|---|---|
 | |
| Born | (1914-10-22)22 October 1914 |
| Died | 22 April 1945(1945-04-22) (aged 30) Ganacker, subcamp ofFlossenbürg concentration camp, Germany |
| Alma mater | University of Straßburg |
| Known for | Feldbau's theorem: afiber bundle over asimplex is trivializable |
| Scientific career | |
| Fields | Mathematics |
| Doctoral advisor | Charles Ehresmann |
Jacques Feldbau was a French mathematician, born on 22 October 1914 inStrasbourg, of anAlsatianJewish traditionalist family. He died on 22 April 1945 at theGanacker Camp, annex of the concentrationcamp of Flossenbürg in Germany. As a mathematician he worked ondifferential geometry andtopology.
He was the first student ofCharles Ehresmann. He is known as one of the founders of the theory offiber bundles. He is the one who first proved that a fiber bundle over asimplex is trivializable and who used this to classify bundles overspheres.[1]
In a paper, written together with Ehresmann, he introduced the notion of anassociated bundle and proved results known today as theexacthomotopysequence of afibration.[2]
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Described byMichèle 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 inStrasbourg, receiving his high school diploma in 1932, and then he started preparatory classes atLycée Kléber. He applied for theÉcole normale supérieure but refused to present himself on Saturday (the Jewish sabbath), and so was not allowed to continue. He enrolled at theUniversity 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 ofCharles Ehresmann in 1939. He was also a pianist and swimmer. becoming a university butterfly-stroke champion in 1939. As soon as the 1930s, Feldbau was participating in a "defence group against anti-Semitism."
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Mobilized in 1939, he became a flying officer in the French Air Force. Demobilized after thearmistice 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 theVichy regime under the Pétain government. He then went to Clermont-Ferrand, where the University of Strasbourg had been evacuated to, where he met his supervisor, Charles Ehresmann. In order to earn a living he gave mathematics lessons and continued his research in topology for his doctoral thesis; he also became a member of the Resistance movement. The status of Jews was one of the additional burdens of Nazi occupation; it quickly became impossible for a scientist labelled as "non- Aryan " to publish under his name. Michèle Audin showed a note to the Proceedings of the Academy of Science, starting with his signature and that of Charles Ehresmann. It was eventually published under the sole name of Ehresmann albeit with mention of the results being obtained "in collaboration with one of his students". Jacques Feldbau subsequently published two short notes in the Bulletin de laSociété Mathématique de France under the pseudonym "Jacques Laboureur" or "Jacques Ploughman". (The name "Feldbau" in German means "agriculture".)
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...
— André Weil, The Apprenticeship of a Mathematician, p. 112
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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 theGestapo in the house of a resistance member, Professor Jean-Michel Flandin. Feldbau himself was not present in the house, but was arrested on 25 June in the morning, when he went to collect hisPhD thesis. He was transferred toDrancy and then deported toAuschwitz, by train No. 60 of 7 October 1943, where he arrived on 10 October. The testimonies of survivors show the moral strength and support he brought to his companions. His mastery of several languages was a great help to him. He would have held seminars in mathematics on Sunday afternoon and a conference on quantum theory.
On 16 January 1945, the camp was evacuated by theSS for death marches westward. Feldbau died ofexhaustion in camp Ganacker, inBavaria, two weeks before the end of the war.
His remains were repatriated in 1957 by his sister, and he was reinterred in Cronenbourg.
At the instigation ofCharles Ehresmann he conducted crucial work inalgebraic topology and specifically on fiber spaces. Amongst its key findings, we note the following fundamental theorem: "a fiber space of asimplex is trivializable "and its corollary, "to give a bundle on asphere 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, writesAndré 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 thehomotopyexact sequence offiber bundles.
The posthumous papers of Feldbau, published by Ehresmann in 1958, also include work onhomotopy groups of higher order, later recovered, and overtaken byJ. 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]
