The first proof that a fiber bundle over a simplex is trivializable was established by Jacques Feldbau, a French mathematician whose research laid essential foundations for the theory of fiber bundles. Working in topology, he collaborated with his mentor Charles Ehresmann to define associated bundles and demonstrate the exact homotopy sequence of a fibration during the period of Nazi occupation.
Early Academic Development
Born in 1914 in Strasbourg, Feldbau attended the Lycée Fustel-de-Coulanges until 1932 before transitioning to the Lycée Kléber. He entered the University of Strasbourg in 1934, where he served as the librarian for the Institute of Mathematics. By 1939, he began doctoral research under the supervision of Charles Ehresmann while participating in an organized group against anti-Semitism.
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Following his 1940 demobilization from the French Armed Forces, exclusionary laws prohibited him from teaching. He relocated to Clermont-Ferrand, where the University of Strasbourg had been evacuated. To circumvent restrictions on Jewish authors, he published research under the pseudonyms Jacques Laboureur and Jacques Ploughman, or through collaborative papers where his contributions were noted by Ehresmann as coming from a student.
Research in Topology
His primary work focused on algebraic topology and fiber spaces. He established that a fiber bundle over a sphere relates to mappings within the group of automorphisms of the fiber. Posthumously, his papers on higher-order homotopy groups were published by Ehresmann in 1958, documenting his efforts in a field where he competed with researchers such as J.H.C. Whitehead.
Deportation and Death
In June 1943, following university protests in Strasbourg, authorities arrested Feldbau. He was transferred to Drancy and subsequently deported to Auschwitz in October 1943. While imprisoned, he held informal seminars on mathematics and quantum theory for fellow inmates. He was transferred again during the 1945 evacuation of the camp and died at the Ganacker concentration camp on 22 April 1945.
Fast facts
- Born: 1914, Strasbourg, France
- Died: 22 April 1945, Ganacker, Germany
- Education: University of Strasbourg, University of Clermont-Ferrand
- Primary Field: Topology
- Pseudonyms: Jacques Laboureur, Jacques Ploughman
- Final Resting Place: Cronenbourg Jewish cemetery
- Doctoral Supervisor: Charles Ehresmann
Questions readers ask
What were Jacques Feldbau's main mathematical achievements?
He is recognized for founding the theory of fiber bundles, proving the trivializability of a fiber bundle over a simplex, and developing the exact homotopy sequence of a fibration.
Why did he publish under pseudonyms?
Due to the 1940 laws of exclusion enforced under the Vichy regime, scientists labeled as non-Aryan were forbidden from teaching and faced significant barriers to publishing research under their own names.
Achievements
- Held posts at French Armed Forces
- Fields: topology
