Timeline for A generalization of covering spaces to fiber bundles with totally path-disconnected fibers
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 10, 2014 at 20:17 | vote | accept | Andrej Bauer | ||
| May 10, 2014 at 19:45 | answer | added | Jeremy Brazas | timeline score: 5 | |
| May 10, 2014 at 9:08 | comment | added | Andrej Bauer | Yes please, I suspect a theorem like the one I attempted to state holds, and I'd like to know where to look. | |
| May 10, 2014 at 3:14 | comment | added | Jeremy Brazas | There are many generalizations of covering space theory out there. Are you looking for examples of such things? | |
| May 10, 2014 at 3:12 | comment | added | Jeremy Brazas | I doubt Theorem 2 is true if you are using the usual notion of fiber bundle that includes local triviality. For one, if $X$ is any locally path connected planar set (like the Hawaiian earring), then there is a "generalized universal covering" $p:\tilde{X}\to X$ with totally path-disconnected fiber $F$ where $G=\pi_1(X)$ acts freely and transitively on $F$ and $\tilde{X}/G\cong X$...but this is far from a fiber bundle since it is not locally trivial. There are even generalizations of coverings (called semicoverings) with discrete fibers that are not locally trivial. | |
| May 9, 2014 at 23:19 | comment | added | Ricardo Andrade | Another small correction: the conclusion of theorem 1 also requires the base space to be semi-locally simply connected. | |
| May 9, 2014 at 22:20 | comment | added | Andrej Bauer | Thanks, fixed. I think the second theorem will need a similar fix. (If it is actually true.) | |
| May 9, 2014 at 22:19 | history | edited | Andrej Bauer | CC BY-SA 3.0 |
added 54 characters in body
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| May 9, 2014 at 21:33 | comment | added | Tom Goodwillie | To make Theorem 1 true you must also require $B$ to be locally path-connected. | |
| May 9, 2014 at 20:41 | history | asked | Andrej Bauer | CC BY-SA 3.0 |