Timeline for Spectral sequence in Adams's book, Theorem 8.2
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Apr 28 at 12:43 | history | edited | Dave Benson | CC BY-SA 4.0 |
Changed Adam's to Adams's twice.
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| Oct 2, 2023 at 23:34 | vote | accept | T. Wildwolf | ||
| Jul 30, 2023 at 19:16 | vote | accept | T. Wildwolf | ||
| Oct 2, 2023 at 23:33 | |||||
| Jul 20, 2023 at 9:43 | history | edited | T. Wildwolf | CC BY-SA 4.0 |
Change of title as eventually it was misleading, I thought it was related to Atiyah-Hirzebruch spectral sequence. Change of some remarks in the question regarding this misleading approach.
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| Jul 19, 2023 at 22:13 | answer | added | John Palmieri | timeline score: 8 | |
| Jul 19, 2023 at 1:09 | history | edited | RobPratt |
edited tags
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| Jul 19, 2023 at 0:13 | comment | added | John Palmieri | It's not clear to me that the spectral sequence in Adams 8.2 is the Atiyah-Hirzebruch spectral sequence. Nonetheless, the higher derived functors ($\lim^2$ for $n \geq 2$) vanish, as Adams explains, and his convergence condition is that $\lim^1$ is zero as well. To verify that condition, the typical way is, as Adams says, to use the Mittag-Leffler condition (the exercise a bit before 8.1). | |
| Jul 18, 2023 at 23:16 | comment | added | T. Wildwolf | I still cannot see why the description of Boardman is the same as that of Adams. Could you elaborate in an answer please? I understand your comment but I cannot relate the explanations of the two books because they seem different. | |
| Jul 18, 2023 at 20:02 | comment | added | John Palmieri | See the bottom of p. 221 (or near the bottom of p. 240 in the new pretty version of Adams book, people.math.rochester.edu/faculty/doug/otherpapers/…): the higher derived functors of lim are zero in this case. | |
| Jul 18, 2023 at 18:26 | history | edited | Daniel Asimov | CC BY-SA 4.0 |
Corrected spelling of J.F. Adams's surname
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| Jul 18, 2023 at 18:17 | comment | added | T. Wildwolf | yes I have read it but he doesn't include a p-th derived limit of $E^{q}(X_{a})$. He provides a criterion for when the spectral sequence converges strongly and it is when $RE_{\infty}=0$, the derived limit of the cycles is zero. | |
| Jul 18, 2023 at 17:33 | comment | added | John Palmieri | Boardman's paper Conditionally Convergent Spectral Sequences (uio.no/studier/emner/matnat/math/MAT9580/v21/dokumenter/…) has a section on the Atiyah-Hirzebruch spectral sequence. | |
| Jul 18, 2023 at 10:46 | history | edited | YCor | CC BY-SA 4.0 |
formatting
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| Jul 18, 2023 at 10:40 | history | asked | T. Wildwolf | CC BY-SA 4.0 |