Timeline for Rational cohomology of a contractible $G$-space with finite stabilizers
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
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| Jan 1, 2018 at 12:22 | comment | added | Arnaud Mortier | Johannes Ebert's answer to this question might help: mathoverflow.net/q/51993 | |
| Nov 11, 2017 at 18:21 | comment | added | mme | The fibers of your projection are $BH$, where $H$ is the stabilizer of the corresponding point. Because $H$ is finite this has trivial rational cohomology, which is why you should think that map is an isomorphism. If I generally had a map with acyclic fibers, I would want to do something sheafy to show it's an isomorphism in homology. Consider the presheaf $\mathcal H$ on the $X/G$ which assigns to $U$ the Q-cohomology of $f^{-1}(U)$, sheafify, take the corresponding spectral sequence from $H^*(X/G;H^*(\mathcal H))$ to $H^*(EG \times_G X)$. Now use that $\mathcal H$ is acyclic. | |
| Nov 11, 2017 at 17:51 | history | asked | user109300 | CC BY-SA 3.0 |