Timeline for Homotopy groups of $S^2$
Current License: CC BY-SA 3.0
19 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 19, 2016 at 7:21 | vote | accept | Roberto Frigerio | ||
| S Aug 24, 2015 at 5:23 | history | suggested | Ali Taghavi | CC BY-SA 3.0 |
I add a tag
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| Aug 24, 2015 at 3:46 | review | Suggested edits | |||
| S Aug 24, 2015 at 5:23 | |||||
| Aug 8, 2015 at 15:27 | answer | added | Ripan Saha | timeline score: 49 | |
| May 12, 2011 at 16:03 | vote | accept | Roberto Frigerio | ||
| Jan 19, 2016 at 7:21 | |||||
| May 9, 2011 at 9:09 | history | edited | Roberto Frigerio | CC BY-SA 3.0 |
added 861 characters in body
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| May 8, 2011 at 15:58 | comment | added | Todd Trimble | @Roberto: thanks! The reasons you give indicate that this is not merely idle curiosity; would you consider putting some of what you wrote in your question? | |
| May 7, 2011 at 8:45 | comment | added | Tilman | @André: Well my vague intuition would be that zero groups will get sparser and sparser but not actually stop. But I don't think anybody knows. | |
| May 6, 2011 at 23:38 | comment | added | André Henriques | @Tilman: Are you saying that the set of $n$ such that $\pi_n(S^0)_{(p)}^{stable}\not = 0$ is infinite? That wold be pretty surprising to me... | |
| May 6, 2011 at 21:42 | comment | added | Roberto Frigerio | @Todd: in fact, it is probably better to say that I was curious, rather than interested. In fact, a student of mine is reading Ivanov's proof that bounded cohomology vanishes for simply connected spaces. Ivanov considers the complex of bounded singular cochains and constructs a chain homotopy between the identity and the null map. The construction of this homotopy involves the description of a Postnikov system for the space considered. In some sense, $S^2$ represents the easiest nontrivial case, and I was just trying to figure out what is happening in this case. | |
| May 6, 2011 at 20:57 | comment | added | Tilman | @André: why? It's not true stably, is it? | |
| May 6, 2011 at 20:20 | answer | added | Hal Sadofsky | timeline score: 25 | |
| May 6, 2011 at 20:00 | comment | added | Dylan Wilson | I assume that if there is a known answer to this question, one would get at it via the EHP sequence? There don't seem to be many techniques other than that to get at unstable homotopy groups... | |
| May 6, 2011 at 19:13 | comment | added | Ryan Budney | @Todd: beyond finiteness of homotopy groups of spheres this seems to be one of the simplest questions you could ask about these groups. So I find it a pretty natural and elementary question. If I was to guess, because of the Berrick-Cohen-Wong-Wu theorem, perhaps Roberto is interested in properties of Brunnian braids. | |
| May 6, 2011 at 18:22 | comment | added | André Henriques | @Tilman: It is not unreasonable to conjecture that for any prime $p$, the set of $n$ such that $\pi_n(S^2)_{(p)}\not = 0$ is finite... So low-dimensional evidence actually does count as evidence. | |
| May 6, 2011 at 16:54 | comment | added | Todd Trimble | Why are you interested? | |
| May 6, 2011 at 16:21 | comment | added | Tilman | Do you have any particular reason to think all the homotopy groups are nontrivial, except for the low-dimensional evidence? | |
| May 6, 2011 at 16:13 | comment | added | André Henriques | Probably an open problem... | |
| May 6, 2011 at 15:34 | history | asked | Roberto Frigerio | CC BY-SA 3.0 |