Timeline for Is every long exact sequence of homotopy groups induced by a fibration?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Sep 3, 2012 at 12:07 | vote | accept | Pierre | ||
| Aug 8, 2012 at 2:04 | comment | added | Mariano Suárez-Álvarez | (He maximizes the diacritic/letter ratio, too...) | |
| Aug 8, 2012 at 2:03 | comment | added | Mariano Suárez-Álvarez | Related: Jan Šťovíček has a beautiful paper (arxiv.org/abs/0906.1286) where he characterizes the long exact sequences of length six which come from the snake lemma. | |
| Aug 8, 2012 at 1:57 | answer | added | Paul | timeline score: 0 | |
| Aug 7, 2012 at 17:19 | comment | added | Pierre | This is precisely what I meant, thanks Paul! (You can probably re-post this as the answer) | |
| Aug 7, 2012 at 4:19 | comment | added | Paul | I understood the question differently: Given $F,E,B$, a map $i:F\to E$, and a long exact sequence of homotopy groups with the map $\pi_q(F)\to \pi_q(E)$ induced by $i$, does there exist a map $p:E\to B$ which realizes this long exact sequence? Any map can be turned into a fibration by replacing the domain by a homotopy equivalent space. So in this interpretation the question boils down to whether the homotopy fiber of $i:F\to E$ is the loop space of $B$. I don't think this is always possible. | |
| Aug 6, 2012 at 9:44 | answer | added | Mark Grant | timeline score: 3 | |
| Aug 6, 2012 at 9:15 | comment | added | Pierre | I edited the question and hope that it is clear now | |
| Aug 6, 2012 at 9:14 | history | edited | Pierre | CC BY-SA 3.0 |
added 277 characters in body
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| Aug 6, 2012 at 8:55 | comment | added | Ralph | What do you mean by "is ... induced" ? | |
| Aug 6, 2012 at 8:44 | history | asked | Pierre | CC BY-SA 3.0 |