Timeline for Getting rid of exceptional fibers by passing to finite covers?
Current License: CC BY-SA 2.5
8 events
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| Aug 27, 2010 at 22:33 | comment | added | Ryan Budney | The caveat is you can only do it after a finite cover of the total space, so it's answering a slightly different question than you asked (the source of my confusion). But the reason is pretty simple. Compare the "bad" orbifolds here: en.wikipedia.org/wiki/Orbifold to the classification of the fiberings of Seifert-fibred manifolds here: math.cornell.edu/~hatcher/3M/3Mdownloads.html and you see the only problems are fiberings of lens spaces, $S^3$, $S^1\times S^2$ all of which have covers where you can replace the Seifert-fibrings with a bundle. | |
| Aug 23, 2010 at 0:59 | comment | added | Zarathustra | How do you know that it's always possible to substitute the fibering over a bad orbifold with a "good" fibering? | |
| Aug 21, 2010 at 23:13 | comment | added | Ryan Budney | Ah, I think my first response (the one that I erased) was the one you were looking for. It's as Ian says, but here is perhaps a slightly more concrete version -- take a lens space like $L_{p,q}$ and its fibering always lifts to a singular fibering of of all of its covering spaces. If you allow yourself the freedom of changing the seifert fibering after you take a covering space, this isn't a problem. | |
| Aug 21, 2010 at 22:54 | comment | added | Ryan Budney | I suppose what one needs to do is check what the bad orbifold types are -- if they're only things like the the non-Hopf fibration fiberings of $S^3$, just replace those Seifert fiberings with the Hopf fibering, and you'd be done. | |
| Aug 21, 2010 at 19:52 | history | undeleted | Ryan Budney | ||
| Aug 21, 2010 at 19:52 | history | edited | Ryan Budney | CC BY-SA 2.5 |
qualify my statement
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| Aug 21, 2010 at 19:05 | history | deleted | Ryan Budney | ||
| Aug 21, 2010 at 19:05 | history | answered | Ryan Budney | CC BY-SA 2.5 |