Timeline for Mayer-Vietoris for local system cohomology
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 29, 2017 at 4:37 | comment | added | Fernando Muro | You need fundamental groupoids in general. | |
| Jul 28, 2017 at 20:39 | comment | added | user2520938 | @Misha Thanks for the recommendations. The fact that in one framework the connectivity of the space is significant, while in the other it isn't, is exactly what confuses me, since I've repeately been told that these frameworks are equivalent... Can you say anything about that? | |
| Jul 28, 2017 at 20:18 | comment | added | Misha | See Brown's "Cohomology of groups" for an algebraic treatment. Or use any book which covers sheaf cohomology, e.g. Bredon's "Sheaf theory". In terms of sheaves, lack of connectivity is a non-issue. | |
| Jul 28, 2017 at 17:23 | comment | added | user2520938 | @OscarRandal-Williams I see. I'm not convinced that we can't though, since this definition supposedly coincides with the sheaf cohomology of the sheaf defined by the local system. Using this sheaf definition we do have a Mayer Vietoris sequence, and hence this should translate back to something phrased in terms of the definition I gave, right? | |
| Jul 28, 2017 at 17:15 | comment | added | Oscar Randal-Williams | You can't and shouldn't: choose a better definition of local system of coefficients and its cohomology. | |
| Jul 28, 2017 at 16:38 | history | asked | user2520938 | CC BY-SA 3.0 |