Timeline for Conditions for underlying space of an orbifold $\Bbb T^n/\Gamma$ to be a sphere?

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12 events

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Apr 13, 2017 at 12:19	history	edited	CommunityBot		replaced http://math.stackexchange.com/ with https://math.stackexchange.com/
Oct 14, 2015 at 0:14	comment	added	Neil Hoffman		I think you could be overlooking one of the conditions of Dunbar when you say 'most' quotients of $T^3$ have underlying space $S^3$. In fact, there are several quotients of $T^3$ with underlying space $S^1\times S^2$, for example the product of the pillowcase $S^2(2,2,2,2)$ and $S^1$. These all turn out to be fibered orbifolds, so Dunbar doesn't focus on them. However, it should be pointed out that $S^2(2,2,2,2) \times S^1$ can cover itself, so 'most' perhaps might be 'most (up to homeomorphism)'.
Aug 14, 2015 at 22:32	history	bounty ended	arivero
Aug 13, 2015 at 16:52	history	edited	Igor Rivin	CC BY-SA 3.0	added five dimensions
Aug 12, 2015 at 17:21	comment	added	arivero		well the underlying manifold must be a manifold, yep, but for the orbifold of course I am happy to allow for conical singularities and usual stuff (I just mention it for benefit of the casual passer-by)
Aug 12, 2015 at 16:34	history	edited	Igor Rivin	CC BY-SA 3.0	added $n=4$ info.
Aug 11, 2015 at 22:38	history	edited	Igor Rivin	CC BY-SA 3.0	more examples
Aug 8, 2015 at 23:46	comment	added	arivero		Hmm having it for n=1,2,3 and possibly 4 starts to signal that dimension is not a main worry. It could have still some argument about having only conical singularities or more extended ones.
Aug 8, 2015 at 23:26	history	edited	Igor Rivin	CC BY-SA 3.0	added 3-d thing.
Aug 8, 2015 at 11:02	history	edited	Igor Rivin	CC BY-SA 3.0	added projective space examples.
Aug 8, 2015 at 10:17	history	edited	Igor Rivin	CC BY-SA 3.0	made small correction, added example
Aug 7, 2015 at 22:42	history	answered	Igor Rivin	CC BY-SA 3.0