Timeline for when is "fibering" preserved under homotopy equivalence
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 9, 2015 at 22:41 | comment | added | ThiKu | Thank you for the correction. So that example may be given as an answer. | |
| Nov 9, 2015 at 17:46 | comment | added | Allen Hatcher | @ThiKu. Of the 28 exotic 7-spheres, only 16 are fiber bundles over $S^4$ with fiber $S^3$. I'm not sure who originally noted this, but it can be deduced from a paper of Itiro Tamura, "Remarks on differentiable structures on spheres" in J. Math. Soc. Japan. 13 (1961), 383-386. | |
| Nov 9, 2015 at 16:19 | comment | added | ThiKu | I guess the question is asking for fibrations over the same base space $B$. For example the exotic 7-spheres are all $S^3$-bundles over $S^4$. In general, however, this seems unplausible: there are many homotopy fibrations that can not be made fibrations and I'd guess that such examples might also be found in the manifolds category, though I don't know of an example. | |
| Nov 9, 2015 at 15:45 | comment | added | Thomas Rot | I think you want to add more conditions, as $E'$ is trivially a fiber bundle over a point. In particular I think you want the homotopy to interact with your fiber bundle structure. | |
| Nov 9, 2015 at 15:37 | history | asked | sara | CC BY-SA 3.0 |