Timeline for Equivariant cohomology vs. invariant cohomology vs. cohomology of quotient space
Current License: CC BY-SA 3.0
3 events
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| Mar 3, 2017 at 18:46 | comment | added | Mark Grant | Note that Andy's Proposition 1.1 works with any coefficients, and asserts an equivalence of cochain complexes $\mathcal{C}^*(X/G)\cong(\mathcal{C}^*(X))^G$, as in my answer. So the outer terms are always equal. Only in Lemma 1.2 are rational coefficients used, to get equality with the middle term. This depends on having a suitable triangulation, of course (so that simplices of $X/G$ correspond to orbits of simplices in $X$). | |
| Mar 3, 2017 at 17:02 | comment | added | Dominic Else | Thanks. Unfortunately the case where the coefficients are a finite Abelian group is really the one I am interested in. | |
| Mar 3, 2017 at 16:58 | history | answered | Andy Putman | CC BY-SA 3.0 |