Timeline for Can Bockstein Spectral Sequence detect multiple summands of the same power, in homology?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 5, 2017 at 13:17 | vote | accept | yoyostein | ||
| Nov 5, 2017 at 12:13 | answer | added | user43326 | timeline score: 2 | |
| Nov 3, 2017 at 18:01 | comment | added | John Palmieri | I'm not sure about the grading. Regarding references, look at the description of the spectral sequence in Mosher and Tangora, Cohomology Operations and Applications in Homotopy Theory. | |
| Nov 3, 2017 at 2:11 | comment | added | yoyostein | @JohnPalmieri Just to check regarding the dimension. Is the following true: if there is one summand $\mathbb{Z}/p$ in $d^r E^r_n$, then there is one summand $\mathbb{Z}/p^r$ in $H_{n-1}(X)$. Is that correct? Thanks! | |
| Nov 2, 2017 at 14:32 | comment | added | yoyostein | Thanks. Is there any reference that mentions this? I checked McCleary's book, it doesn't seem to have it. | |
| Nov 2, 2017 at 14:29 | comment | added | John Palmieri | If the differential is nonzero on two linearly independent classes, then each of those classes corresponds to a different summand. So I suppose you want to know the rank of the differential as a linear map; the rank should be the number of summands. | |
| Nov 2, 2017 at 14:16 | history | asked | yoyostein | CC BY-SA 3.0 |