Timeline for first Chern class of complex vector bundles and first Pontrjagin class of quaternionic vector bundles
Current License: CC BY-SA 3.0
21 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Dec 24, 2015 at 16:01 | comment | added | Jiangnan Yu | Your name is so interesting :D | |
| Nov 19, 2015 at 14:26 | answer | added | Robert Bruner | timeline score: 4 | |
| Oct 12, 2015 at 17:04 | history | reopened |
Robert Bryant Joonas Ilmavirta Stefan Kohl♦ Andrey Rekalo darij grinberg |
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| Oct 12, 2015 at 3:02 | review | Reopen votes | |||
| Oct 12, 2015 at 17:04 | |||||
| Oct 6, 2015 at 12:50 | comment | added | Gil Kalai | Regardless of this particular question, in my opinion, "standard characteristic class stuff" like "standard applications of spectral sequences" like "standard facts about Floer homology" etc. are research-level mathematics as far as mathoverflow is concerned. | |
| Oct 6, 2015 at 11:55 | review | Reopen votes | |||
| Oct 6, 2015 at 14:31 | |||||
| Oct 6, 2015 at 11:41 | comment | added | Robert Bryant | It it probably worth pointing out that there is no nontrivial normal subgroup $\mathrm{SSp}(\mathbb{H},n)\subset \mathrm{Sp}(n)$ (other than the center, which is discrete) because the group $\mathrm{Sp}(n)$ is simple. Thus, there is no interpretation of $p_1(\xi)=0$ as a condition for reducing the structure group of a quaternionic vector bundle $\xi$ to such a subgroup. | |
| Oct 6, 2015 at 11:41 | history | edited | Gil Kalai | CC BY-SA 3.0 |
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| Oct 6, 2015 at 10:41 | vote | accept | QSR | ||
| Oct 6, 2015 at 9:20 | history | closed |
Allen Knutson Qiaochu Yuan David Roberts♦ Stefan Kohl♦ Marco Golla |
Not suitable for this site | |
| Oct 6, 2015 at 6:29 | comment | added | QSR | Sorry, Prof. Yes, this is what I want to express. | |
| Oct 6, 2015 at 6:29 | history | edited | QSR | CC BY-SA 3.0 |
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| Oct 6, 2015 at 6:27 | comment | added | Sebastian Goette | Could you please explain your definition $SU(\mathbb H,n)$? The notation is nonstandard. I did not find it on the wikipedia page in the link. And to relate to Sullivan's answer: quaternion vector bundle means vector bundle with an $\mathbb H$ action by scalars, doesn't it? So the group $Sp(n)\hat\times Sp(1)$ will not appear in this context. | |
| Oct 6, 2015 at 5:52 | history | edited | QSR | CC BY-SA 3.0 |
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| Oct 6, 2015 at 4:24 | history | edited | QSR | CC BY-SA 3.0 |
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| Oct 6, 2015 at 4:18 | comment | added | mme | Crossposted from MSE. | |
| Oct 6, 2015 at 4:01 | answer | added | Dennis Sullivan | timeline score: 9 | |
| Oct 6, 2015 at 2:19 | review | Close votes | |||
| Oct 6, 2015 at 9:20 | |||||
| Oct 6, 2015 at 2:06 | comment | added | Allen Knutson | "the structure group" isn't well-defined, unless you put a metric on it and ask about the holonomy group, in which case the answers are "false". You can ask whether the structure group can be reduced to $SU(n,\mathbb C$ or $\mathbb H)$, in which case the answers are "true". This is standard characteristic class stuff, as in Milnor's book or Husemoller's, not research-level. | |
| Oct 6, 2015 at 1:00 | history | asked | QSR | CC BY-SA 3.0 |