Timeline for Fiber product of spaces and cohomology
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Oct 26, 2023 at 10:12 | comment | added | Matthias Ludewig | So the idea is that if $H^*(Z, R)$ is free over $H^*(X, R)$, then all $Tor^i$ groups are zero for $i\geq 1$, so the spectral sequence stabilizes on the $E_2$ page. But I don't know about these graded Tor groups to be sure whether this works. | |
| Oct 25, 2023 at 16:20 | comment | added | Mark Grant | Yes, it surely exists but it is the identification of the initial and final pages which might be easier with field coefficients. | |
| Oct 25, 2023 at 8:48 | comment | added | Matthias Ludewig | Does that exist if $R$ is not a field? | |
| Oct 25, 2023 at 7:10 | comment | added | Mark Grant | Are you familiar with the Eilenberg-Moore spectral sequence? I think something like this appears in the set up, for instance in McCleary's book. | |
| Oct 25, 2023 at 6:51 | vote | accept | Matthias Ludewig | ||
| Oct 23, 2023 at 12:33 | answer | added | Tom Goodwillie | timeline score: 2 | |
| Oct 22, 2023 at 18:00 | comment | added | Matthias Ludewig | Say, yes! Although I am happy to restrict to a class of spaces where this does not matter. | |
| Oct 22, 2023 at 12:45 | comment | added | Martin Brandenburg | Singular cohomology? | |
| Oct 21, 2023 at 20:35 | comment | added | Matthias Ludewig | Feel free to make assumptions on the spaces. | |
| Oct 21, 2023 at 20:34 | history | edited | Matthias Ludewig | CC BY-SA 4.0 |
edited title
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| Oct 21, 2023 at 19:22 | comment | added | Tom Goodwillie | You might want to assume that the spaces are simply connected. If $X$ is acyclic (same homology as a point) but not contractible, and if $Y$ and $Z$ are contractible, then $W$ will not be connected. | |
| Oct 21, 2023 at 19:19 | history | edited | Tom Goodwillie | CC BY-SA 4.0 |
added 1 character in body
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| Oct 21, 2023 at 18:47 | history | asked | Matthias Ludewig | CC BY-SA 4.0 |