Timeline for Infinite loop spaces
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 1, 2016 at 15:17 | answer | added | user51223 | timeline score: 0 | |
| Dec 12, 2013 at 16:53 | answer | added | user43326 | timeline score: 2 | |
| Sep 14, 2013 at 2:24 | comment | added | Lennart Meier | I cannot answer your question, but consider the folloing example: $X=B\mathbb{Z}/2$, $Y= B\mathbb{Z}/4$ and $f$ the map induced by the non-trivial group homomorphism $\mathbb{Z}/2\to \mathbb{Z}/4$. As $\Omega X \simeq \mathbb{Z}/2$ and $\Omega Y \simeq \mathbb{Z}/4$, the map $\Omega f$ has a left inverse up to homotopy. But there can be no left inverse as an H-map; therefore, $f$ has no left-inverse. This does not answer your question because while $X$ and $Y$ are infinite loop spaces, they are not $Q$ of something. But do you have reason to believe your conjecture to be true? | |
| Sep 3, 2013 at 18:55 | history | asked | András Szűcs | CC BY-SA 3.0 |