Timeline for What are the uses of the homotopy groups of spheres?
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20 events
| when toggle format | what | by | license | comment | |
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| Feb 11, 2022 at 15:00 | answer | added | Andrea Ferretti | timeline score: 4 | |
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
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| Mar 15, 2016 at 6:59 | comment | added | Bruno Stonek | In this article by Kapranov arxiv.org/pdf/1512.07042v1.pdf , notably in page 23, there a table showing the "significance" of the first four stable stems. | |
| May 10, 2015 at 16:19 | answer | added | Mark Grant | timeline score: 10 | |
| Apr 29, 2010 at 1:00 | answer | added | Daniel Moskovich | timeline score: 13 | |
| Apr 28, 2010 at 23:34 | answer | added | Igor Belegradek | timeline score: 14 | |
| Apr 28, 2010 at 20:45 | comment | added | Andrew Stacey | tea.mathoverflow.net/discussion/371/… | |
| Apr 28, 2010 at 20:37 | answer | added | Tim Perutz | timeline score: 29 | |
| Apr 28, 2010 at 17:34 | answer | added | rat | timeline score: 4 | |
| Apr 28, 2010 at 16:15 | comment | added | Andrea Ferretti | Well, I'd say more than related. | |
| Apr 28, 2010 at 16:05 | answer | added | José Figueroa-O'Farrill | timeline score: 26 | |
| Apr 28, 2010 at 14:35 | comment | added | j.c. | This question seems related: mathoverflow.net/questions/16495/… | |
| Apr 28, 2010 at 13:49 | answer | added | Paul Siegel | timeline score: 49 | |
| Apr 28, 2010 at 13:13 | answer | added | Tyler Lawson | timeline score: 23 | |
| Apr 28, 2010 at 12:24 | answer | added | Pete L. Clark | timeline score: 12 | |
| Apr 28, 2010 at 12:10 | comment | added | Steve Huntsman | Here is a (silly) application of FLT due to Schultz that is on Dick Lipton's blog. Proposition. If $n \ge 3$, then $\sqrt[n]{2}$ is irrational. Proof: suppose $\sqrt[n]{2} = z/y$ for $z$ and $y$ positive integers. Taking $n$th powers yields that $2 = z^n/y^n$, so $y^n + y^n = z^n$. By FLT, there is a contradiction. $\Box$ See rjlipton.wordpress.com/2010/03/31/april-fool | |
| Apr 28, 2010 at 12:07 | comment | added | Andrew Stacey | @Pete: I agree with your second sentence completely. However, if you had turned it round, I would have been unhappy. My contention (and I feel as though it's getting more exposure than it's worth!) is that for something to convey lots of information, it must be complicated in some way. (I don't like the word "deep", but that's just a personal dislike.) As for your emphasised sentence, again I'm in complete agreement. But nonetheless, I'd like to know if they have had significant applications! If nothing else, I could sell my subject a bit better than I do at the moment! | |
| Apr 28, 2010 at 12:02 | comment | added | Harry Gindi | Well, they could potentially allow us to compute homotopy group(oid)s like homology groups if we use the higher Van Kampen theorem(s) à la Ronnie Brown, but this sort of computation is still going to be extremely laborious (and probably highly impractical) given that n-groupoids/crossed complexes don't really avail themselves to explicit computation. Of course we'd have to actually compute the homotopy groupoids rather than the homotopy groups of the spheres, but it doesn't seem like such a stretch to be able to compute the whole n-groupoid from having all of the homotopy groups. | |
| Apr 28, 2010 at 11:54 | comment | added | Pete L. Clark | As I wrote in a previous comment, I find your link between complication and usefulness to be quite strange. Just because something is complicated doesn't mean that it conveys more information. Maybe you mean "deep" instead. Certainly there's lots of evidence that the homotopy groups of spheres have a potentially infinite richness of algebraic and topological information: therefore, they are indubitably worthy of study. But have they had significant applications? So far as I know they haven't, and there's nothing wrong with that. Fermat's last theorem has no applications whatsoever... | |
| Apr 28, 2010 at 11:27 | history | asked | Andrew Stacey | CC BY-SA 2.5 |