Timeline for What is the homotopy fiber of the map from a space to its James construction?
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7 events
| when toggle format | what | by | license | comment | |
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| May 14, 2013 at 1:21 | answer | added | Dai Tamaki | timeline score: 2 | |
| Apr 19, 2013 at 13:53 | comment | added | MatanP | Thanks for your comments. It seems there is not a known answer for this question, as John implicitly claimed above. | |
| Apr 17, 2013 at 22:57 | comment | added | John Klein | There is not even a known identification of the homotopy cofiber $C$ of $e_X$ in general. There are some partial results: its suspension $\Sigma C$ is weak equivalent to $\Sigma (X\wedge \Omega \Sigma X)$. In the metastable range (approximately 3 times the connectivity of $X$), the cofiber coincides with the "co-join," i.e., the holim of the diagram $\Sigma X \to \Sigma X \vee \Sigma X \leftarrow \Sigma$ given by the two inclusions. | |
| Apr 17, 2013 at 20:38 | comment | added | Callan McGill | I believe for $X=S^{n}$ then one can get some answers p-locally by looping the EHP sequence. In general I am not sure what can be said. | |
| Apr 17, 2013 at 18:19 | comment | added | Fernando Muro | * is the join, ie the suspension of the smash product. | |
| Apr 17, 2013 at 17:09 | comment | added | Konrad Voelkel | I have the feeling that an analogous result would involve the homotopy cofiber of $\eta$, not the homotopy fiber. By the way, is $\ast$ the wedge product? | |
| Apr 17, 2013 at 15:29 | history | asked | MatanP | CC BY-SA 3.0 |