Timeline for When was the word "stable" first used to describe stable homotopy theory?
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9 events
| when toggle format | what | by | license | comment | |
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| May 12, 2014 at 8:18 | comment | added | nsrt | @HiroLeeTanaka There is no such word. The closest is that he defines that $\pi_dS^e$ "belongs to the k-stem", where $k=d-e$. | |
| May 9, 2014 at 18:05 | comment | added | Hiro Lee Tanaka | @nsrt -- what word, if any, does Freudenthal use to describe the phenomenon of homotopy groups stabilizing? | |
| May 9, 2014 at 1:24 | answer | added | Peter May | timeline score: 3 | |
| May 8, 2014 at 13:21 | comment | added | Lennart Meier | Earlier references: Thom uses it in 'Quelques propriétés globales des variétés différentiables' (1954) for the homotopy groups of his "Thom spectrum" and Serre uses it in 'Cohomologie modulo 2 des complexes d'Eilenberg-MacLane' (1953) for the stable (co)homology groups of Eilenberg-MacLane spaces (later spectra). You also find the word 'stable' in Serre's 'Homologie Singuliere Des Espaces Fibres', but there it is stable under other operations than suspension-related ones. | |
| May 8, 2014 at 13:15 | comment | added | Lennart Meier | One early reference is Bott, An application of the Morse theory to the topology of Lie groups (1956). It is not in Spanier, Whitehead, A first approximation to homotopy theory (1953), where the introduce the Spanier-Whitehead category. 1962 it was well-known enough that Whitehead could call his ICM-talk "Some aspects of stable homotopy theory." | |
| May 8, 2014 at 8:21 | comment | added | nsrt | In his paper, Freudenthal does not use the word "stable" (="stabil" in German) or any similar word. | |
| May 8, 2014 at 7:53 | comment | added | Drew Heard | Maybe the answer is somewhere in: math.uiuc.edu/K-theory/0321/history.pdf (But probably better to just wait for Peter to come along and answer anyway...) | |
| May 8, 2014 at 7:05 | history | edited | Hiro Lee Tanaka | CC BY-SA 3.0 |
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| May 8, 2014 at 6:59 | history | asked | Hiro Lee Tanaka | CC BY-SA 3.0 |