Timeline for Pairing in Group Cohomology [closed]
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Sep 8, 2016 at 12:11 | history | closed |
Ryan Budney Jan-Christoph Schlage-Puchta Franz Lemmermeyer R.P. Chris Godsil |
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| Sep 7, 2016 at 18:57 | comment | added | user37663 | @AlexB. : Thank you.. I will read that.. | |
| Sep 7, 2016 at 18:49 | comment | added | Alex B. | Among number theorists, a canonical reference is the chapter of Atiyah-Wall on group cohomology in Cassels-Fröhlich. Another good reference is Ken Brown's book "Cohomology of Groups". | |
| Sep 7, 2016 at 18:40 | review | Close votes | |||
| Sep 8, 2016 at 12:11 | |||||
| Sep 7, 2016 at 18:34 | comment | added | user37663 | @AlexB. : Ok. For time being i assume it is a typo... If there is any serious result in next chapters that depends on this heavily I would ask here.. By your website, you seem to be working on number theory.. Can you suggest some notes about cup products... | |
| Sep 7, 2016 at 18:27 | comment | added | Alex B. | By definition, ${\rm Hom}(B,C)$ is the submodule of ${\rm Hom}_{\mathbb Z}(B,C)$ on which $G$ acts trivially, so there is a $G$-module structure on it, the trivial one. So your interpretation via restriction does make sense, but a typo still seems more likely. It is actually much more common to write ${\rm Hom}$ for all $\mathbb{Z}$-linear homs, and ${\rm Hom}_G$ for $G$-homs. | |
| Sep 7, 2016 at 18:00 | comment | added | user37663 | @darijgrinberg : I would be happy if that is the case.... How much sure are you about this? | |
| Sep 7, 2016 at 13:21 | comment | added | darij grinberg | This just sounds like a typo in the book. (Which can very well get repeated over and over -- authors often write formulas by copypasting.) | |
| Sep 7, 2016 at 12:10 | history | edited | user37663 | CC BY-SA 3.0 |
added 178 characters in body
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| Sep 7, 2016 at 12:05 | comment | added | user37663 | It can be that.. I am not sure @GregoryArone | |
| Sep 7, 2016 at 12:02 | comment | added | Gregory Arone | I have not read Babakhanian, so I am only guessing. But could it be that he meant that there is a $G$-map $\mbox{Hom}(B,C) \to \mbox{Hom}_{\mathbb Z}(B,C)$ and this is what induces the pairing? Here $Hom(B,C)$ is considered a $G$-module with the trivial action, and the map is inclusion of fixed points. | |
| Sep 7, 2016 at 11:54 | history | asked | user37663 | CC BY-SA 3.0 |