Tudor Ganea
Tudor Ganea (1922–1971) was a Romanian mathematician, known for his work in algebraic topology, especially homotopy theory. Ganea left Communist Romania to settle in the United States in the early 1960s. He taught at the University of Washington.
Work
In 1957, Ganea published in the Annals of Mathematics a short, yet influential paper with Samuel Eilenberg, in which the Eilenberg–Ganea theorem was proved and the celebrated Eilenberg–Ganea conjecture was formulated. The conjecture is still open.
Just before he died, Ganea attended the Symposium on Algebraic Topology, held February 22–26, 1971 at the Battelle Seattle Research Center, in Seattle. At the symposium, he was not able to give a talk, but he did distribute a preprint containing a list of unsolved problems. One of these problems, regarding the Lusternik–Schnirelmann category, came to be known as Ganea's conjecture. Many particular cases of this conjecture were proved, until Norio Iwase provided a counterexample in 1998.
References
- Samuel Eilenberg, Tudor Ganea, On the Lusternik–Schnirelmann category of abstract groups, Annals of Mathematics, 2nd Ser., 65 (1957), no. 3, 517 – 518
- Tudor Ganea, Some problems on numerical homotopy invariants, Lecture Notes in Math. 249 (Springer, Berlin, 1971), pp. 13 – 22
- Norio Iwase, "Ganea's conjecture on Lusternik–Schnirelmann category", in Bulletin of the London Mathematical Society, 30 (1998), no.6, 623 – 634
- (Romanian) Gabriela Adameşteanu, Interview with Aurora Cornu (Ganea's fiancée during the 1960s), in 22, May–June 2006
Quote
My algebraic topology professor, Tudor Ganea, used to say that "mathematics progresses by faith and hard work, the former augmented and the latter diminished by what others have done".
From: "Eightfold Way: The Sculpture", by Helaman Ferguson with Claire Ferguson, in The Eightfold Way: The Beauty of Klein's Quartic Curve, edited by Silvio Levy, MSRI Publications, vol. 35, 1998