Timeline for First group homology with general coefficients
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Mar 11, 2015 at 7:15 | answer | added | Sergei Ivanov | timeline score: 10 | |
| Apr 19, 2012 at 10:42 | vote | accept | Earthliŋ | ||
| Apr 18, 2012 at 20:19 | answer | added | user1437 | timeline score: 14 | |
| Apr 18, 2012 at 17:06 | comment | added | Andy Putman | There is a nice description of the twisted first cohomology group as crossed homomorphisms modulo principal crossed homomorphisms. But there really isn't a particularly nice description of the twisted first homology group. | |
| Apr 18, 2012 at 13:11 | comment | added | Jim Conant | @s.barmeier: Sorry I got the wrong term in the complex. This is what happens when I answer before my morning coffee. My answer gave $H_0(G)$ which gives a quotient of $M$, namely the coinvariants $M_G$. | |
| Apr 18, 2012 at 12:59 | comment | added | Earthliŋ | But $\mathbb Z[G]\otimes_{\mathbb Z[G]}M$ is just $M$, no? A quotient of $M$ does sound not too bad. Thanks for your answers, I'll ask my pencil for more insights. | |
| Apr 18, 2012 at 12:48 | comment | added | Jim Conant | You'll get a certain quotient of $\mathbb Z[G]\otimes_{\mathbb Z[G]}M$ by the boundary operator. In the case of twisted coefficients the two parts of the tensor will be mixed up, so you won't have a nice factorization. | |
| Apr 18, 2012 at 12:42 | comment | added | Earthliŋ | In Brown's book I can only find the statement with trivial coefficients... Do you have a page reference? Or are you suggesting I should calculate $H_1$ via the bar resolution, which I can't imagine has a straight-forward answer for an arbitrary action. | |
| Apr 18, 2012 at 12:26 | history | edited | Earthliŋ | CC BY-SA 3.0 |
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| Apr 18, 2012 at 12:18 | comment | added | berl13 | You will find the answer in Brown's book "Cohomology of groups". When the action is not trivial you have to work with twisted coefficients. | |
| Apr 18, 2012 at 10:55 | history | asked | Earthliŋ | CC BY-SA 3.0 |