Timeline for What is the importance of $\pi_{i}G$?
Current License: CC BY-SA 3.0
13 events
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| Jul 23, 2012 at 16:02 | comment | added | Paul Reynolds | A search of the literature indicates that while $\pi_2G = 0$ does follow from Bott's work in Milnor's book, it was in fact proved by E.Cartan in 1911 before Bott was even born. | |
| Jul 22, 2012 at 7:20 | history | edited | Kerry | CC BY-SA 3.0 |
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| Jul 22, 2012 at 7:19 | comment | added | Kerry | I am really embarrassed, my memory is not accurate; the papers asked whether $\pi_{1}G$ is free instead. Sorry for raisng the wrong question at here. | |
| Jul 22, 2012 at 5:06 | answer | added | Zhaoting Wei | timeline score: 6 | |
| Jul 22, 2012 at 4:55 | comment | added | Mariano Suárez-Álvarez | Can you list couple of examples of papers which use the hypothesis that $\pi_2G\neq0$? | |
| Jul 22, 2012 at 4:51 | comment | added | Mariano Suárez-Álvarez | The vanishing of $\pi_2$ was discussed at least once in MO: google might be of help finding the thread, which was very enlightening! | |
| Jul 22, 2012 at 2:50 | history | edited | Kerry | CC BY-SA 3.0 |
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| Jul 22, 2012 at 2:27 | comment | added | Kerry | You mean simple ones, or any? I did read Bott's collective papers but never seen this theorem. I shall check the link. | |
| Jul 22, 2012 at 2:25 | comment | added | Akhil Mathew | Incidentally, $\pi_2 G = 0$ for any Lie group; this is a theorem of Bott. See mathoverflow.net/questions/8957/homotopy-groups-of-lie-groups for a very nice discussion or Milnor's book "Morse Theory." | |
| Jul 22, 2012 at 2:21 | comment | added | Kerry | I see the problem, corrected. | |
| Jul 22, 2012 at 2:21 | history | edited | Kerry | CC BY-SA 3.0 |
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| Jul 22, 2012 at 2:17 | comment | added | Will Sawin | Is that symplectic group supposed to have an even dimension? | |
| Jul 22, 2012 at 2:12 | history | asked | Kerry | CC BY-SA 3.0 |