Timeline for Continuity property for Čech cohomology
Current License: CC BY-SA 4.0
6 events
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| Oct 27, 2020 at 19:52 | comment | added | Xindaris | Okay, from what I can tell Eilenberg and Steenrod define Čech cohomology purely in terms of coefficients in a module rather than a presheaf; possibly their book predates sheaf theory in general. I wonder whether I should refine my question to ask whether sheaf cohomology satisfies a continuity property, since some sources appear to identify Čech cohomology as an "approximation" to that which is equal on nice enough spaces. | |
| Oct 27, 2020 at 16:03 | comment | added | Xindaris | I wasn't sure I had access to that before, but I was able to get it. It looks like the negative answer is for spaces that aren't compact, but the paper also seems to say the continuity property for compact hausdorff spaces is proved in Eilenberg and Steenrod's Foundations of algebraic topology. I tried reading that before without much success, but I suppose I can try again. | |
| Oct 27, 2020 at 15:30 | comment | added | Tyrone | Did you look at Watanabe's paper that Matthias Wendt cites in your link? It seemed to say that the answer to your question is $i)$ no, in general, $ii)$ yes, if you are smart. Of course Watanabe works with constant coefficients. | |
| Oct 26, 2020 at 18:20 | history | edited | YCor | CC BY-SA 4.0 |
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| Oct 26, 2020 at 16:27 | review | First posts | |||
| Oct 26, 2020 at 16:52 | |||||
| Oct 26, 2020 at 16:25 | history | asked | Xindaris | CC BY-SA 4.0 |