Talk:Orbifold

From Wikipedia, the free encyclopedia

The stub is mathematically incorrect. What it describes is the so-called "good" orbifold, but there are bad ones also.

Be bold; why don't you add the info about the good and the bad ones? Dysprosia 10:31, 28 Sep 2003 (UTC)

Are we talking about differentiable manifolds here? Also, I'm not sure whether the word "discrete" adds anything to the definition. AxelBoldt 19:52, 18 Jan 2004 (UTC)

There's a whole topic of hyperbolic orbifolds (replace R^n with H^n, etc.); I know just enough to mention this might be important, but don't feel qualified enough to offer a presentation. Just wanted to throw the idea out there.

Should, "finite quations of Rⁿ," not be "finite quotients of Rⁿ?"

---

The formal definition talks about "linear actions of a finite group on an open subset of Rⁿ". What's the meaning of "linear" here? Also, I find it surprising that the compatibility condition does not refer to the group actions at all. AxelBoldt 17:39, 23 Jun 2004 (UTC)

I changed it to linear transformation. On the group action, I think it is still correct, the compatibility condition for the group actions follow from it (let me know if I'm wrong). Tosha 19:42, 23 Jun 2004 (UTC)

So we're talking about a finite group of linear transformations acting on an open subset U of Rⁿ? That seems a bit strange to me: there aren't many such actions, because most linear transformations won't map U bijectively onto U. Maybe we should allow a finite group of diffeomorphisms? Is there a good book to read up on these things, maybe something by Thurston? Thanks, AxelBoldt 09:55, 25 Jun 2004 (UTC)

sure, there aren't many such actions for general U, but given an action one can choose an invariant U, I do not see a problem here. If you want to change def. to more stadard(?) it is fine, but I like this one... If you change to diffeomorphsm it will give the same orbifold, but the def will become mor complecated. I do not know a good ref. I'm not sure but it seems that Thurston was mostly interested in 3-d case. I took a def from some paper (now I do not remember which) and modifyed it a bit Tosha 12:09, 5 Jul 2004 (UTC)

[edit] Homogeneous space

Isn't it the case that the base space (Euclidean space modulo group of linear xforms) is just an example of a homogeneous space? Perhaps I'm missing something, but I'm having trouble figureing out why euclidean space is singled out in this article, instead of having a more general definition for a homogeneous space. In fact, the "string theory" definition seems to be trying to say this, without actually blurting out that M/G must be a homogeneous space in order to have the usual properties. linas 16:37, 19 September 2006 (UTC)