Timeline for Manifold whose universal covering is a sphere but which is not a space form?
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 18, 2012 at 21:05 | answer | added | Ian Agol | timeline score: 10 | |
| Sep 18, 2012 at 16:35 | vote | accept | Thomas Richard | ||
| Sep 18, 2012 at 16:34 | comment | added | Thomas Richard | Ok, thanks to all ! @Agol: why not ? even if I suspect that might be out of my reach... | |
| Sep 18, 2012 at 14:34 | comment | added | Ian Agol | Are you interested when the universal cover of $M$ is an exotic sphere (and of course $M$ is smooth)? | |
| Sep 18, 2012 at 13:44 | comment | added | Igor Belegradek | There are other examples. You might like fake $RP^5$'s of nonnegative curvature of Grove-Ziller, see Theorem G in math.upenn.edu/~wziller/papers/groveziller.ps. Of course, the existence of fake $RP^5$'s was known to topologists long ago, but the above paper gives a geometric construction. Is that what you seek? | |
| Sep 18, 2012 at 13:34 | comment | added | Mark Grant | Interestingly, the book Igor Rivin links to defines a space form to be "a manifold whose universal cover is a sphere" (on the first page of the introduction). I guess that here we mean "manifold which is the orbit space of a free action on a sphere". | |
| Sep 18, 2012 at 13:13 | comment | added | Igor Rivin | The reference I suggest is a book, so this is probably as gentle as you can hope for. This was one of the guiding problems in topology for a couple of decades, so I don't think there is a really easy way of getting there. | |
| Sep 18, 2012 at 12:58 | comment | added | Thomas Richard | Thanks to both Igors for your answers. I'm not familiar with these topics, so I'll have to dig a bit into these papers to understand. Does there exist a more elementary construction ? | |
| Sep 18, 2012 at 12:32 | answer | added | Igor Belegradek | timeline score: 13 | |
| Sep 18, 2012 at 12:20 | answer | added | Igor Rivin | timeline score: 11 | |
| Sep 18, 2012 at 12:09 | history | edited | j.c. | CC BY-SA 3.0 |
fix title?
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| Sep 18, 2012 at 11:54 | history | asked | Thomas Richard | CC BY-SA 3.0 |