Timeline for Cohomology of a stratified projective bundle
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 13, 2023 at 14:55 | comment | added | Jason Starr | I have seen a version of that spectral sequence in one of Dan Petersen’s articles. | |
| S Jul 3, 2023 at 17:06 | history | bounty ended | CommunityBot | ||
| S Jul 3, 2023 at 17:06 | history | notice removed | CommunityBot | ||
| Jun 25, 2023 at 15:41 | history | edited | LSpice | CC BY-SA 4.0 |
Capitalise title; typo
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| S Jun 25, 2023 at 15:07 | history | bounty started | IMeasy | ||
| S Jun 25, 2023 at 15:07 | history | notice added | IMeasy | Draw attention | |
| Jun 22, 2023 at 7:32 | comment | added | IMeasy | @Donu: could you give me at least one reference about that spectral sequence? thank you | |
| Jun 18, 2023 at 16:21 | comment | added | IMeasy | OK, perfect!.... er... I mean, thank you, that would be awesome! | |
| Jun 18, 2023 at 15:50 | comment | added | Donu Arapura | I should probably make this an answer, and I will when I have more time. | |
| Jun 18, 2023 at 15:47 | comment | added | Donu Arapura | Perfect means that the restriction maps $H^i (X_j)\to H^i(X_{j-1})$ are surjective, where $\ldots X_{j-1}\subset X_j\ldots$ are the strata. I learned this terminology from a paper of Atiyah and Bott. | |
| Jun 18, 2023 at 15:00 | comment | added | IMeasy | @DonuArapura, what does "perfect" mean for the stratification? and how does the situation get better in that case? and BTW what is the spectral sequence that abuts to that? (too many questions, I know) | |
| Jun 18, 2023 at 14:43 | comment | added | Donu Arapura | The spectral sequence, or a more elementary argument, will give you the Euler characteristic of $X$. | |
| Jun 18, 2023 at 14:40 | comment | added | Donu Arapura | There would be a spectral sequence abutting to the cohomology of $X$, with $E_1$ term the relative cohomology of strata. And unless you know that the stratification is "perfect", that's the best you can hope for. | |
| Jun 18, 2023 at 14:05 | history | asked | IMeasy | CC BY-SA 4.0 |