Timeline for Cokernel of the stable J-homomorphism at odd primes
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Mar 6, 2014 at 14:52 | comment | added | Craig Westerland | A much simpler argument: at the prime $p$, the only contributions to the image of $j$ are in degrees of the form $* = 2(p-1)k-1$, which cannot be the dimension of Cohen's family. | |
| Mar 6, 2014 at 14:33 | comment | added | Craig Westerland | Yes -- it is entirely contained in the $Ext^3$ line of the Adams spectral sequence. As Mahowald mentions, Adams showed that the J-homomorphism produces at most finitely many elements in $Ext^k$ for any $k$. | |
| Mar 6, 2014 at 14:22 | comment | added | Igor Belegradek | Does Cohen's family survive in the cokernel of $J$? | |
| Mar 6, 2014 at 5:29 | comment | added | Craig Westerland | ... and I got cut off: Hunter-Kuhn's "Mahowaldean families of elements in stable homotopy groups revisited." The Adams spectral sequence names for these classes are $h_0 b_j$, their dimension is $2(p-1)p^{j+1}+2p-5$, and they have order precisely $p$. | |
| Mar 6, 2014 at 5:22 | comment | added | Craig Westerland | There is an odd-primary analogue of the $\eta_j$ family discovered by Ralph Cohen in "Odd primary infinite families in stable homotopy theory." That text is hard to find on the internet, but a more recent approach to the subject is Hunter-Kuhn | |
| Mar 6, 2014 at 4:52 | comment | added | Igor Belegradek | Well, I just thought odd primes are easier. For my purposes I may have to choose a large enough prime, but in any case I did not know of the family, and am grateful for the info. | |
| Mar 6, 2014 at 4:48 | comment | added | Craig Westerland | Ack, sorry; I never even saw the odd-primary part of your request. | |
| Mar 6, 2014 at 4:43 | comment | added | Craig Westerland | I think that it's order 2; this is at least suggested by the Adams spectral sequence (since $h_0 h_1 h_j = 0$), but I don't actually know. | |
| Mar 6, 2014 at 4:41 | history | edited | Craig Westerland | CC BY-SA 3.0 |
fixed grammer.
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| Mar 6, 2014 at 4:32 | comment | added | Igor Belegradek | Thank you! Is the order of $\eta_j$ known? | |
| Mar 6, 2014 at 4:13 | history | answered | Craig Westerland | CC BY-SA 3.0 |