Timeline for Why is it difficult to obtain the next differential in a spectral sequence?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Sep 12, 2017 at 3:44 | answer | added | Dexter Chua | timeline score: 13 | |
| Sep 11, 2017 at 22:41 | comment | added | Tyler Lawson | I think perhaps the point is that many spectral sequences come in a form where we know the exact couple exists, and we know E_r and perhaps d_r, but we do not know the rest of the exact couple (indeed, we are often trying to compute A or something like it). | |
| Sep 11, 2017 at 22:27 | comment | added | Sebastian Goette | The correct statement seems to be "there is an algorithm that, given $(A,E,i,j,k)$ spits out $(A',E',i',j',k')$" (this is maybe one of the best known constructions). But I wonder how helpful such a statement is for spectral sequences (like Adams spectral sequence) where the exact couple is not so easy to describe. | |
| S Sep 11, 2017 at 22:16 | history | suggested | Ali Taghavi |
I add a tag
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| Sep 11, 2017 at 22:00 | review | Suggested edits | |||
| S Sep 11, 2017 at 22:16 | |||||
| Sep 11, 2017 at 18:25 | comment | added | Fernando Muro | If a SS comes from an exact couple then all information is contained therein, but a page of a spectral sequence can only compute the terms of the next page. | |
| Sep 11, 2017 at 18:25 | comment | added | Mariano Suárez-Álvarez | Your hope that «there is some algorithm that from $(E_r,d_r)$ spits out $(E_{r+1},d_{r+1})$ is simply not realized. It is trivial to produce examples of spectral sequences which coincide only up to some page. | |
| Sep 11, 2017 at 18:23 | comment | added | John Smith | @FernandoMuro That's what I thought until Hatcher said: "This information is contained in the original exact couple, but often in a way which is difficult to extract, so in practice one usually seeks other ways to compute the subsequent differentials." | |
| Sep 11, 2017 at 18:20 | comment | added | Fernando Muro | A term of a spectral sequence is the homology of the previous one, but the differential cannot be computed from the previous terms and deferentials. It's just not defined like that. | |
| Sep 11, 2017 at 18:19 | review | First posts | |||
| Sep 11, 2017 at 18:24 | |||||
| Sep 11, 2017 at 18:15 | history | asked | John Smith | CC BY-SA 3.0 |