Timeline for Criterion for alternation of the linking form
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 12, 2018 at 15:55 | comment | added | Michael Albanese | Such an example would provide an answer to this question. | |
| Jun 12, 2018 at 12:44 | comment | added | Michael Albanese | @YonatanHarpaz: You're right. I realised this last night, but I couldn't think of an example where $w_3 = 0$ but $W_3 \neq 0$. Do you know of such an example? | |
| Jun 12, 2018 at 9:47 | comment | added | Yonatan Harpaz | There is a small subtlety here to take into account: the $w_3$ appearing in Browder's theorem lives in $H^3(X,\mathbb{Z}/2)$, and is equal to $Sq^1w_2$. The vanishing of $w_3$ is hence not equivalence to $w_2$ having an integral lift, but to $w_2$ having a lift to $H^2(X,\mathbb{Z}/4)$. The obstruction to $w_2$ having an integral lift is a certain class in $H^3(X,\mathbb{Z})$ which lifts $w_3$. | |
| Jun 10, 2018 at 16:32 | history | edited | j.c. | CC BY-SA 4.0 |
add link
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| Jun 10, 2018 at 14:48 | history | answered | Michael Albanese | CC BY-SA 4.0 |