Timeline for Equivariant cohomology of fixed points using the localisation theorem
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Jul 9 at 19:54 | answer | added | Nicholas Kuhn | timeline score: 2 | |
| Jul 9 at 13:22 | answer | added | Andy Putman | timeline score: 1 | |
| Jul 9 at 10:51 | answer | added | Jason Starr | timeline score: 3 | |
| Jul 7 at 12:05 | comment | added | Jason Starr | Also, this $\mathbb{S}^1$-bundle over $BG$ is pulled back from a $\mathbb{S}^1$-bundle over $B\mathbb{S}^1$, and this space is simply connected. So the derived pushforward of the constant coefficient sheaf $\mathbb{Z}$ is (quasi-isomorphic) to the complex of constant sheaves of the cohomology of the fiber. So the hypotheses for the Thom-Gysin sequence are satisfied also on the pullback. | |
| Jul 7 at 11:40 | comment | added | Jason Starr | The $\mathbb{S}^1$-bundle over $X_G$ is pulled back from $BG$. So the cohomology class is the pullback of the “first Chern class” of that circle bundle over $BG$. | |
| Jul 7 at 9:54 | comment | added | 0hliva | @JasonStarr Also, if we have this Thom-Gysin sequence, the map $H_G^r(X)\to H_G^{r+2}(X)$ is given by the cup-product $t\smile (-)$ with $t\in H^2_G(X)$. But Tom-Dieck says that this map is the cup-product with some $t\in H^2(BG)$ (page 198 in Transformation Groups). | |
| Jul 7 at 9:50 | comment | added | 0hliva | @JasonStarr so the Thom-Gysin sequence associated to the bundle $S^1\to X\times_G S^1\to X_G$? If yes, why is the action of $\pi_1X_G$ on $X\times_G S^1$ trivial so that we can apply the Thom-Gysin sequence? | |
| Jul 6 at 20:59 | comment | added | Jason Starr | Actually it is the Thom-Gysin Sequence. | |
| Jul 6 at 18:31 | comment | added | Jason Starr | That looks like the Wang Sequence. | |
| Jul 6 at 14:33 | history | edited | YCor | CC BY-SA 4.0 |
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| S Jul 6 at 12:53 | review | First questions | |||
| Jul 6 at 13:42 | |||||
| S Jul 6 at 12:53 | history | asked | 0hliva | CC BY-SA 4.0 |