Timeline for Cohomology with group ring coefficients and compact support
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Mar 13, 2020 at 20:24 | comment | added | Tyler Lawson | @Laura This previous question appears to indicate that this might be VIII.7.5 in Ken Brown's "Cohomology of groups"? mathoverflow.net/questions/102654/… I don't currently have access to the book to check. | |
| Mar 13, 2020 at 19:30 | comment | added | Laura | @JohannesHuisman: That's what I meant, and I hope it was clear from the context. It would be perverse to take a trivial local system that also happened to be a module over the fundamental group... | |
| Mar 13, 2020 at 19:29 | comment | added | Laura | @TylerLawson: That's a good example -- I thought I had worked out $\mathbb{Z}$ acting on $\mathbb{R}$, but looking back over my notes I had screwed it up. Still very interested if you ever figure this out. | |
| Mar 12, 2020 at 15:25 | comment | added | Johannes Huisman | Nothing to do with your question, but doesn't the (co)homology of the complex $D^\bullet$ rather compute the cohomology of $X/G$ with coefficients in a local system locally isomorphic to $\mathbf{Z}[G]$, instead of constant coefficients $\mathbf{Z}[G]$? | |
| Mar 10, 2020 at 14:52 | comment | added | Tyler Lawson | Hi Laura, the complex $D^\bullet$ doesn't coincide on the nose with the compactly supported cochains. E.g. taking $\Bbb R$ with its action of $\Bbb Z$, the complex $D^\bullet$ contains the 1-dimensional cochain $f$ such that: $f(\sigma) = 1$ if $\sigma(t) = a t$ for some $a$, and $f(\sigma) = 0$ otherwise. I haven't been able to determine whether it still computes compactly supported cohomology; I suspect not, but haven't been able to solve it. | |
| Mar 4, 2020 at 22:40 | review | First posts | |||
| Mar 5, 2020 at 4:46 | |||||
| Mar 4, 2020 at 22:35 | history | asked | Laura | CC BY-SA 4.0 |