Timeline for Group cochains invariant under the action of the symmetric group
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Sep 14, 2020 at 17:05 | history | edited | Steven Sam | CC BY-SA 4.0 |
changed an n to k
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| Feb 27, 2014 at 12:15 | answer | added | César Galindo | timeline score: 8 | |
| Jan 9, 2014 at 21:50 | comment | added | Eric Wofsey | I don't know a published reference, but I addressed the analogous question for singular cohomology of arbitrary spaces here. | |
| Jan 9, 2014 at 18:53 | comment | added | Kevin Walker | I think there are different conventions, related by the "upper triangular" change of coordinates $g_i' = g_1 g_2 \cdots g_i$. The version I gave agrees with the Wikipedia article, these notes, and various other sources. I don't have access to the book you mention, so if you wanted to expand on the homogeneous/inhomogeneous cochain remark, I would be interested to hear more. | |
| Jan 9, 2014 at 16:49 | comment | added | Filippo Alberto Edoardo | I guess the point is the isomorphism between cohomology defined with homogeneous and inhomogeneous cochains (you find it, for instance, in Neukirch-Schmidt-Wingberg's "Cohomology of Number Fields", Chap I, §2) - I can try to write down a precise answer if you do not see what I mean. By the way, don't you have a degree shifting in your definition of $C^k=\mathrm{Map}(G^{k+1},A)$? Also, I guess you have a typo in the definition of $\delta$, the intermediate term should be $(-1)^if(g_1,\dots,g_{i-1},g_{i+1},\dots,g_{k+1})$, shouldn't it? | |
| Jan 9, 2014 at 14:38 | history | edited | Kevin Walker | CC BY-SA 3.0 |
fixed some typos; added small clarifications
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| Jan 8, 2014 at 20:02 | history | asked | Kevin Walker | CC BY-SA 3.0 |