Timeline for Induced maps on homotopy groups by self maps of $\mathbb{CP}^n$
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 29, 2018 at 17:51 | comment | added | mme | @JasonDeVito It sounds like the contribution was all your own :) | |
| Oct 29, 2018 at 17:36 | comment | added | Jason DeVito - on hiatus | My board is currently covered with attempts at using Freudenthal in exactly the way you suggest (and with exactly the same predicted answer). I must just be writing down the wrong commutative diagram... | |
| Oct 29, 2018 at 17:34 | comment | added | mme | @JasonDeVito I think you can apply Freudenthal suspension and the fact that a degree $n$ map suspends to a degree $n$ map to see that it's multiplication by $n^2$ = multiplication by $n$ (since $n^2 = n$ mod 2). | |
| Oct 29, 2018 at 17:33 | comment | added | Jason DeVito - on hiatus | Do you happen to know (or know a reference) for what map $\pi_{k+1}(S^k)\rightarrow \pi_{k+1}(S^k)$ is induced from a degree $n$ map $S^k\rightarrow S^k$. I know the proof (using Whitehead products) for $k=2$, but I'm not sure how to generalize. Of course, for larger $k$, $\pi_{k+1}(S^k)\cong \mathbb{Z}_2$.... | |
| Aug 9, 2018 at 22:10 | comment | added | Sigur | Thanks so much for you attention. Let me read/study what you wrote. | |
| Aug 9, 2018 at 21:54 | history | answered | mme | CC BY-SA 4.0 |