Timeline for Is this exact sequence known?
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Jan 9, 2023 at 12:21 | comment | added | Pedro | @MikhailBorovoi Perhaps the "direct check" is reproducing the proof of the Snake Lemma? | |
| Jan 9, 2023 at 2:24 | history | edited | LSpice | CC BY-SA 4.0 |
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| Oct 21, 2022 at 11:38 | answer | added | Mikhail Borovoi | timeline score: 4 | |
| Sep 4, 2022 at 18:28 | vote | accept | Mikhail Borovoi | ||
| Sep 4, 2022 at 18:13 | vote | accept | Mikhail Borovoi | ||
| Sep 4, 2022 at 18:14 | |||||
| Sep 4, 2022 at 17:56 | answer | added | SashaP | timeline score: 5 | |
| Sep 4, 2022 at 17:12 | history | edited | Mikhail Borovoi | CC BY-SA 4.0 |
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| Sep 4, 2022 at 17:00 | comment | added | Mikhail Borovoi | @SashaP: The answer that I have is by direct checks on cocycles (four pages of calculations). The preprint will appear in arXiv on Wednesday September 7, and I have enough time to replace my direct checks by your nice proof. | |
| Sep 4, 2022 at 16:56 | comment | added | Mikhail Borovoi | @SashaP: Yes, this is exactly the kind of answer I am looking for. Please kindly post an answer with as much details as possible! | |
| Sep 4, 2022 at 16:26 | comment | added | SashaP | On the other hand, the six groups appearing in the desired sequence appear on the 1st page of this spectral sequence and, since both $Tor_0(H_1(\Gamma,M_3),\mathbb{Q}/\mathbb{Z})$ and $Tor_0(H_1(\Gamma,M_2),\mathbb{Q}/\mathbb{Z})$ are zero (because these homology groups are annihilated by the order of $\Gamma$), no non-zero differentials on page 2 and onward can touch these 6 groups, which gives the desired sequence. | |
| Sep 4, 2022 at 16:26 | comment | added | SashaP | I'm not sure if this is a kind of answer that you're looking for or if I'm repeating the proof you already have, possibly in a different language. We can get this exact sequence from the spectral sequence corresponding to the derived functor of tensor product with $\mathbb{Q}/\mathbb{Z}$ applied to the long exact sequence of $\Gamma$-homology corresponding to the given SES. On the one hand this long exact sequence is an acyclic complex so the spectral sequence must converge to zero. | |
| Sep 4, 2022 at 15:42 | history | edited | Mikhail Borovoi | CC BY-SA 4.0 |
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| Sep 4, 2022 at 14:14 | history | edited | Mikhail Borovoi | CC BY-SA 4.0 |
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| Sep 4, 2022 at 13:46 | history | asked | Mikhail Borovoi | CC BY-SA 4.0 |