Timeline for cohomology of BG, G compact Lie group
Current License: CC BY-SA 3.0
17 events
| when toggle format | what | by | license | comment | |
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| Mar 14, 2014 at 14:10 | answer | added | archipelago | timeline score: 8 | |
| Apr 17, 2011 at 7:48 | comment | added | Dr Shello | I think the tag "mathematical-physics" is there to attract the flavor of answer of interest to the OP (as well as, perhaps, his/her backround), viz, e.g. Figueroa-O'Farrill's answer. | |
| Apr 17, 2011 at 7:04 | comment | added | Dave Anderson | A small correction: the third line should be $H^\ast(BT;{\Bbb R}) = {\Bbb R}[t_1,...,t_n]$, where the $t_i$'s are Chern roots, all of degree 2. Morally, the inclusion $H^\ast(BT) \hookrightarrow H^\ast(BG)$ is a manifestation of the splitting principle, i.e., "any vector bundle splits (compatibly with extra structure)", so characteristic classes can be written in terms of Chern roots. | |
| Apr 17, 2011 at 2:53 | answer | added | Allen Knutson | timeline score: 18 | |
| Apr 16, 2011 at 18:39 | answer | added | Johannes Ebert | timeline score: 9 | |
| Apr 15, 2011 at 9:26 | answer | added | Ralph | timeline score: 7 | |
| Apr 15, 2011 at 7:47 | answer | added | Mark Grant | timeline score: 17 | |
| Apr 15, 2011 at 7:39 | comment | added | David Roberts♦ | @klw1026 - see my second comment. And when I say $G$ I mean the cohomology of $BG$. | |
| Apr 15, 2011 at 6:54 | comment | added | Kevin Wray | @David - Yes, that is what seen/heard. But I did not need the full isom. (I thought), just the inclusion (hence why I dropped the Weyl action). So, I guess the right question would've been: What is $H^*(BU(1)\times\cdot\cdot\cdot\times BU(1),\mathbb{R})$, since the torus group $T\cong U(1)\times\cdot\cdot\cdot\times U(1)$, right? | |
| Apr 15, 2011 at 6:46 | comment | added | David Roberts♦ | Retagged . | |
| Apr 15, 2011 at 6:45 | history | edited | David Roberts♦ |
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| Apr 15, 2011 at 6:45 | comment | added | David Roberts♦ | For the groups $U(n), SU(n) and Sp(n)$ the result follows from calculating the integral cohomology rings and seeing that they are polynomial rings on even degree generators. This is 4D.4 in Hatcher. But I believe the OP is thinking of the approach outlined in e.g. the first paragraph of arxiv.org/abs/0903.4865 - this is due to Borel I believe. | |
| Apr 15, 2011 at 6:43 | comment | added | Kevin Wray | Yes, sorry about tagging it mp. I was thinking about where this surfaces - which happened to be some papers on Chern-Simons theory. | |
| Apr 15, 2011 at 6:38 | answer | added | José Figueroa-O'Farrill | timeline score: 12 | |
| Apr 15, 2011 at 6:34 | comment | added | David Roberts♦ | @Andy - perhaps it is the direction the OP is coming from... which doesn't make it right however. | |
| Apr 15, 2011 at 5:48 | comment | added | Andy Putman | Why is this tagged mathematical-physics? | |
| Apr 15, 2011 at 5:29 | history | asked | Kevin Wray | CC BY-SA 3.0 |