Timeline for Whitehead product and a homotopy group of a wedge sum
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 27, 2021 at 8:43 | vote | accept | Anthony | ||
| Apr 27, 2021 at 2:38 | answer | added | John Klein | timeline score: 10 | |
| Apr 24, 2021 at 21:20 | comment | added | Nicholas Kuhn | Look up the Hilton-Milnor theorem (or really just Hilton's 1955 paper). | |
| Apr 23, 2021 at 20:14 | comment | added | Tyler Lawson | To proceed you probably first need an excision-type result, identifying $\pi_{n+k+2}(X \times Y, X \vee Y)$ with $\pi_{n+k+2}(X \wedge Y)$. Then you can use the Hurewicz theorem + Kunneth formula to identify $\pi_{n+k+2}(X \wedge Y)$ with $\pi_{n+1}(X) \otimes \pi_{k+1}(Y)$. | |
| Apr 23, 2021 at 20:00 | comment | added | Mark Grant | I don't recall the proof exactly, but it might help to know that the homotopy fibre of $X\vee Y\to X\times Y$ is $\Omega X\ast \Omega Y$ (the join of the loop spaces). | |
| Apr 23, 2021 at 15:37 | history | asked | Anthony | CC BY-SA 4.0 |