Timeline for Using the Serre spectral sequence - moving between $\mathbb{Z}/2$ and $\mathbb{Z}$ information
Current License: CC BY-SA 4.0
5 events
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| Jun 17, 2020 at 7:59 | comment | added | user43326 | OK, it wasn't really Kunneth, but the thing is $H^*(F.Z/2)$ is a (graded) vector space over $Z/2$, so taking cohomology with $H^*(F.Z/2)$ coefficients is same as taking cohomology with $Z/2$-coefficients and then tensoring with $H^*(F.Z/2)$. | |
| Jun 17, 2020 at 6:48 | comment | added | user101010 | @user43326 What do you mean by using the Kuenneth here? The only Kuennth that comes to mind for me here is for computing (co)homology of products. The reason these classes are drawn is not really because they hit the bottom (see the next spectral sequence that is pictured in that section), but because they are involved in the computation of the cohomology of the total space through degree 8. | |
| Jun 16, 2020 at 19:10 | comment | added | user43326 | As to your first question, since we are talking about the mod 2 cohomology, we can simply use the Kunneth to fill in. The reason why Hatcher bothered to mark these classes is, presumably, becaute they hit the claas in the bottom line. | |
| Jun 16, 2020 at 17:33 | history | edited | Arun Debray |
added {spectral-sequences} tag
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| Jun 16, 2020 at 16:09 | history | asked | user101010 | CC BY-SA 4.0 |