Timeline for Computation of homotopy groups of spheres via Pontryagin-Thom
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 27, 2015 at 19:35 | answer | added | Andy Putman | timeline score: 8 | |
| Oct 6, 2013 at 13:17 | comment | added | András Szűcs | Pontryagin's mistake was, that he thought that the Arf invariant was a homomorphism instead of a quadratic function (that is $q(x+y) \ne q(x) + q(y)$, but $q(x+y) = q(x) + q(y) + xy).$ | |
| Oct 6, 2013 at 13:03 | comment | added | András Szűcs | The too much time Pontryagin spent on developing foundation could be related to the fact that the first published version of the computation of the second stable homotopy group contained a mistake and that led to an incorrect result for it. That was corrected more than ten years later. | |
| Oct 6, 2013 at 12:53 | comment | added | András Szűcs | Naturally Pontryagin's book does not contain the computation of the third stable homotopy group of spheres, which is Rokhlin's result, but it does the computation of the first two groups. | |
| Jul 16, 2013 at 21:41 | answer | added | András Szűcs | timeline score: 4 | |
| Nov 19, 2012 at 10:12 | comment | added | Liviu Nicolaescu | I still believe that Pontryagin's book is by far the best presentation of the subject. Unlike more modern books, Pontryagin makes a systematic effort to describe the key ideas unobscured by technicalities. At the same time no technical detail is missing. This is some achievement! Even the foundational part is a joy to read. You should compare Pontryagin's presentation of the proof of Sard's theorem to Milnor's. The proofs are identical, but for the first time I saw somebody who could outdo Milnor in presenting the proof. | |
| Nov 19, 2012 at 8:32 | answer | added | Mike-Doherty | timeline score: 5 | |
| Nov 19, 2012 at 7:38 | answer | added | Chris Gerig | timeline score: 7 | |
| Nov 19, 2012 at 6:34 | answer | added | David C | timeline score: 7 | |
| Nov 19, 2012 at 5:55 | history | asked | N Zhao | CC BY-SA 3.0 |