Timeline for Explicit representatives for Borel cohomology classes of a compact Lie group?
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| when toggle format | what | by | license | comment | |
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| Jul 30 at 5:35 | comment | added | jdc | I think I understand what you mean by "Borel" now. I was brought up to interpret it as something different ("Borel equivariant: the (singular) cohomology of the Borel construction associated to an action). Did you wind up working this out? | |
| Feb 28 at 17:47 | comment | added | Kevin Walker | Borel cohomology is (roughly) the $G$-equivariant cohomology of a point, or the ordinary cohomology of $BG$. Perhaps the Cartan 3-form is related to the explicit cocycle I'm looking for, but I don't see how to turn it (the Cartan 3-form) into a function $G^3\to R/Z$. Again, I might be missing something obvious. | |
| Feb 28 at 13:46 | comment | added | jdc | I'm not familiar with this definition of Borel cohomology, so I'm not certain if this helps any, or if it will come as news, but an explicit generator for the de Rham cohomology space $H^3(G)$, for $G$ compact simple Lie, is given by the Cartan 3-form (see, e.g <mathoverflow.net/questions/62998/…). | |
| Feb 28 at 13:20 | history | edited | Kevin Walker | CC BY-SA 4.0 |
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| Feb 27 at 19:17 | history | asked | Kevin Walker | CC BY-SA 4.0 |