Timeline for Cup product in Tate Cohomology Ring
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 12, 2019 at 14:44 | vote | accept | C. Zhihao | ||
| Sep 12, 2019 at 8:34 | answer | added | Mark Grant | timeline score: 4 | |
| Sep 11, 2019 at 22:39 | comment | added | mme | The periodicity is proved in extreme generality in section 16 of Greenlees-May's book on Tate cohomology, see in particular Corollary 16.7: for any commutative ring $A$, if $G$ acts freely and orientation preservingly on a sphere of dimension $n$, then the cup product with a certain class $[\chi_V] \in H^{n+1}(G;A)$ induces an isomorphism $\hat H^*(G;A) \cong \hat H^{*+n+1}(G;A)$. You can drop the oriented assumption if $A$ is an $\Bbb F_2$-algebra. I don't remember if they talk about the ring structure though. | |
| Sep 11, 2019 at 22:16 | history | asked | C. Zhihao | CC BY-SA 4.0 |