Tudor Ganea

Tudor Ganea (October 17, 1922–August 1971, Seattle, Washington)[1] 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.[2] 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.

By 1958, Ganea and his mentee, Israel Bernstein, were the two leading algebraic topologists in Romania.[3] Later that year at an international conference on geometry and topology in Iași, the two met Peter Hilton, starting long mathematical collaborations. Ganea emigrated to Western Europe in 1961, and later came to the United States.

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.[4]

References

  1. ↑ Biographical information
  2. ↑ (in Romanian) Gabriela Adameșteanu, Interview with Aurora Cornu (Ganea's fiancée during the 1960s), in 22, May–June 2006.
  3. ↑ Israel Berstein, June 23, 1926—September 22, 1991
  4. ↑ Iwase, Norio (1998). "Ganea's conjecture on Lusternik–Schnirelmann category". Bulletin of the London Mathematical Society. 30 (6): 623–634. doi:10.1112/S0024609398004548. MR 1642747.

Publications

  • Eilenberg, Samuel; Ganea, Tudor (1957). "On the Lusternik–Schnirelmann category of abstract groups". Annals of Mathematics. 2nd Ser. 65 (3): 517–518. doi:10.2307/1970062. MR 0085510.
  • Ganea, Tudor; Hilton, Peter J.; Peterson, Frank P. (1962). "On the homotopy-commutativity of loop-spaces and suspensions". Topology. 1: 133–141. doi:10.1016/0040-9383(65)90021-2. MR 0150774.
  • Ganea, Tudor (1965). "A generalization of the homology and homotopy suspension". Commentarii Mathematici Helvetici. 39: 295–322. doi:10.1007/BF02566956. MR 0179791.
  • Ganea, Tudor (1967). "Lusternik–Schnirelmann category and strong category". Illinois Journal of Mathematics. 11: 417–427. MR 0229240.
  • Ganea, Tudor (1971), Some problems on numerical homotopy invariants, Lecture Notes in Mathematics, 249, Berlin: Springer, pp. 13–22, MR 0339147

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

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