Timeline for mod p (odd) cohomology of dihedral groups
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 5, 2019 at 17:38 | vote | accept | Jacksbabypig | ||
| Feb 4, 2019 at 22:54 | comment | added | Denis Nardin | @MikeMiller Aaand there was still a residue mistake (I assumed that the Sylow subgroup wouldn't be trivial). Fixed now :) | |
| Feb 4, 2019 at 22:49 | history | edited | Denis Nardin | CC BY-SA 4.0 |
added 2 characters in body
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| Feb 4, 2019 at 22:48 | comment | added | mme | I thought your answer was fine as it was, I just wanted to add something for anybody passing by :) Some small points: there is a surviving $C_p$ somewhere. Because $S^1$ is a non-discrete space as well as a group, can I suggest writing $H^2(BS^1; \Bbb F_p)$ on the second-to-last displayed line (and maybe similarly for $BC_n$) to avoid confusion? | |
| Feb 4, 2019 at 22:32 | comment | added | Denis Nardin | @MikeMiller Thanks! I was trying to avoid using the fiber sequence $C_p\to S^1\to S^1$ to give a more "algebraic" proof, but you're right, the argument flows much better if we embrace it. | |
| Feb 4, 2019 at 22:32 | history | edited | Denis Nardin | CC BY-SA 4.0 |
Inserted simplification in the proof
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| Feb 4, 2019 at 17:50 | comment | added | mme | Everything is correct. Your argument can be streamlined by working with the LHSS for $\Bbb Z/n \to D_{2n} \to \Bbb Z/2$ directly instead of passing to a $p$-Sylow, then reducing to the case of $S^1$, which has an automorphism extending negation on $\Bbb Z/n$. The induced map of this automorphism (complex conjugation) on $S^1$ is complex conjugation on $\Bbb{CP}^\infty$, so $\sigma b = -b$. | |
| Feb 4, 2019 at 17:27 | history | edited | Denis Nardin | CC BY-SA 4.0 |
added 3 characters in body
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| Feb 4, 2019 at 17:27 | comment | added | Denis Nardin | I am oscillating between being convinced that this answer is correct and being convinced that it is complete bunk. Right now I think it's correct and I've got to leave now, so I'll offer it to you clemence.. | |
| Feb 4, 2019 at 17:25 | history | undeleted | Denis Nardin | ||
| Feb 4, 2019 at 17:13 | history | deleted | Denis Nardin | via Vote | |
| Feb 4, 2019 at 17:07 | history | undeleted | Denis Nardin | ||
| Feb 4, 2019 at 17:07 | history | edited | Denis Nardin | CC BY-SA 4.0 |
Removed erroneous argument using the Bockstein
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| Feb 4, 2019 at 16:14 | history | deleted | Denis Nardin | via Vote | |
| Feb 4, 2019 at 15:43 | history | answered | Denis Nardin | CC BY-SA 4.0 |