Timeline for Induced map of degree $k$ self map of a sphere in the higher homotopy groups
Current License: CC BY-SA 4.0
4 events
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| Oct 30 at 13:07 | comment | added | Thomas Rot | Dear Tyrone, thank you for your excellent answer, I didn't see that question before. This tells me how to think about these maps. Of course this involves many computations for all unstable groups. This is more complicated than that I hoped for, but I guess that was to be expected. Again, thanks for the pointers! | |
| Oct 29 at 13:07 | comment | added | Tyrone | What I can add is that an odd-dimensional sphere localised at an odd prime is an H-space. Thus for an odd-dimensional sphere, the degree $k$ map acts as multiplication by $k$ on odd primary components. The 2-primary case is not completely understood. | |
| Oct 29 at 12:55 | comment | added | Tyrone | See my answer here. The method works in higher dimensions up to knowing certain Whitehead products and Hopf invariants. This doesn't quite answer your question, though. | |
| Oct 29 at 12:45 | history | asked | Thomas Rot | CC BY-SA 4.0 |