Timeline for Strong convergence of whole-plane spectral sequences
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 5, 2018 at 23:35 | comment | added | John Rognes | Elements in $C^0 = \bigoplus_p D^{p,-p}$ are finite sums $\sum_p x_p$ with $x_p \in D^{p,-p}$. In the completions we discussed above you allow formal sums where $p$ is either bounded below, or bounded above (depending on the case). By completing at "both ends" I meant that you would allow formal sums, without bounds, amounting to the product $\prod_p D^{p,-p}$. Similarly for $C^1 = \bigoplus_p D^{p,1-p}$, completing to $\prod_p D^{p,1-p}$. | |
| Feb 5, 2018 at 21:02 | comment | added | Steve | Thanks for your answer, what did you mean by 'at "both ends"'? | |
| Feb 5, 2018 at 19:59 | comment | added | John Rognes | I don't see how to complete the double complex $D$. You could consider a completion of the total complex $C$, at "both ends", but it would not arise from the filtrations giving rise to the two spectral sequences. | |
| Feb 5, 2018 at 1:12 | comment | added | Steve | Sorry I meant "...so that the cohomology of the completions of the total complexes $\widehat{C_1}^\alpha$ and $\widehat{C_1}^\beta$ are the same?" | |
| Feb 5, 2018 at 1:04 | comment | added | Steve | May I ask if it's possible to 'complete' the double complex $D$ in the first place, say $D_1$, so that the completions of the total complex $\widehat{C_1}^\alpha$ and $\widehat{C_1}^\beta$ are the same? and that $H^*(\widehat{C_1}^\alpha)=H^*(\widehat{C_1}^\beta)=H^*(\widehat{C}^\beta)\not=0$? | |
| Jan 29, 2018 at 23:24 | comment | added | Steve | Thanks very much for your answer. This clears up alot of confusion for me. | |
| Jan 29, 2018 at 23:18 | vote | accept | Steve | ||
| Jan 27, 2018 at 22:57 | history | answered | John Rognes | CC BY-SA 3.0 |