Timeline for Spectral sequences: opening the black box slowly with an example
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Nov 27, 2017 at 2:34 | comment | added | Eric Peterson | Yeah, it is a matter of indexing convention. Vakil follows the "Serre grading" and this example follows the "Adams grading". (Denis's complaint is still outstanding, though.) | |
| Nov 25, 2017 at 20:49 | comment | added | anon | (I'm reading Vakil's notes, so maybe it's just some different indexing convention.) | |
| Nov 25, 2017 at 20:33 | comment | added | anon | I have a very silly question (still very new to spectral sequences): isn't the third differential $d_3$ supposed to go from $E_3^{p,q}$ to $E_3^{p+3,q-2}$? In your diagram, it looks like your differential goes 3 times up, 1 times left, instead of 3 times up, 2 times left. | |
| Aug 22, 2017 at 6:54 | comment | added | Eric Peterson | It's quite OK! This also bothered me for a long time, but I never wrapped my head around where the dimension skew was coming from. Danny Shi figured this out, but I was too thick to understand what he was getting at. He's the right person to ask—I'll push him to come and edit the answer. | |
| Aug 21, 2017 at 8:07 | comment | added | Denis Nardin | @EricPeterson Sorry for dredging this old answer back. I was trying to think all details through and it seems to me that you are identifying the $\eta$ in $H^0(C_2;\pi_1\mathbb{S})$ with the $\eta$ in $H^1(C_2;\pi_2KU)$ but in fact the first class is not sent to the second (of course the map $\pi_1\mathbb{D}\,\mathbb{RP}^\infty_+\to \pi_1KO$ sends $\eta$ to $\eta$ but they live in different filtration degrees). Do you know how to fill in the details to go from the $d_2$ differential in the first spectral sequence to the $d_3$ differential in the second? | |
| Aug 14, 2017 at 21:19 | history | edited | j.c. | CC BY-SA 3.0 |
fix image
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| Jun 21, 2013 at 8:06 | comment | added | Sean Tilson | Your boxed comment is really important. What is being alluded do are universal examples in the style of Bousfield and Kan. | |
| Jun 20, 2013 at 15:09 | comment | added | Eric Peterson | Thank you! Mike and Mike and Mark know some really compelling stuff --- they're the phenomenal ones. :) | |
| Jun 20, 2013 at 15:06 | history | edited | Eric Peterson | CC BY-SA 3.0 |
added 63 characters in body
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| Jun 20, 2013 at 13:19 | comment | added | David White | This is a phenomenal answer. Thanks for sharing! | |
| Jun 20, 2013 at 2:41 | history | edited | Eric Peterson | CC BY-SA 3.0 |
added 294 characters in body
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| Jun 20, 2013 at 2:29 | history | answered | Eric Peterson | CC BY-SA 3.0 |