Timeline for Strong Convergence vs Conditional Convergence for Spectral Sequences (Is there a simple explanation?)
Current License: CC BY-SA 3.0
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| Dec 1, 2017 at 18:45 | comment | added | Justin Noel | Unless I'm missing something, as long as for each target group H_k, the part of the spectral sequence calculating E_\infty H_k, has no differentials in or out after the nth page (which can depend on k) then the spectral sequence will strongly converge under these conditions. | |
| Dec 1, 2017 at 18:25 | comment | added | Justin Noel | I second Drew's recommendation. The paper is complex, but wonderful. The key ingredients are: A spectral sequence should be associated to a good filtration: the intersection/union of the filtration that should be 0 is very much 0 and conditional convergence gives this by definition. You should also be sure that the respective union/intersection of your filtration actually calculates what you are looking for. In practice, checking these conditions is easy. Under these conditions the only thing to check is that | |
| Nov 16, 2017 at 19:07 | comment | added | Drew Heard | The usual reference for these types of things is Boardman's 'Conditionally convergent spectral sequences' - citeseerx.ist.psu.edu/viewdoc/…. The remark after Theorem 7.1 suggests the answer to your question is that such a spectral sequence strongly converges. | |
| Nov 16, 2017 at 15:16 | history | asked | yoyostein | CC BY-SA 3.0 |