# Tag Info

## Hot answers tagged orbifolds

Accepted

### Is every rational realized as the Euler characteristic of some manifold or orbifold?

Products of 2-orbifolds with manifolds will do the trick. There are 2-orbifolds of Euler characteristic $1/n$ (take a quotient of $S^2$ by a rotation of order $2n$). Then take a product with a ...
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### Is every rational realized as the Euler characteristic of some manifold or orbifold?

The answer for connected 2-dimensional orbifolds is no. Euler characteristic is $$\chi(O)=\chi(M)-\sum\left(1-\frac{1}{q}\right)-\frac{1}{2}\sum\left(1-\frac{1}{p}\right),$$ where $p,q\geq 2$ are ...
• 79.5k
Accepted

### What is an example of an orbifold which is not a topological manifold?

It is quite easy to give an example in real dimension $4$. In fact, it was shown by D. Mumford in the paper The topology of normal singularities of an algebraic surface and a criterion for ...
• 62.5k
Accepted

### Condensed / pyknotic approach to orbifolds?

Great question! I think the answer ought to be yes. But I must also make a disclaimer that I don't really know what orbifolds are, and the comments by David Roberts make be believe that what I thought ...
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### why most of the angles are right

Let the root system be $v_1$, …, $v_n$ with all elements normalized to be length $1$. So $\langle v_i, v_i \rangle =1$, we have $\langle v_i, v_j \rangle \leq - \cos (\pi/3) = -1/2$ for at least $n$ ...
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### Does the torus $T^d$ 2-fold cover an orbifold $Q^d$ with underlying space $S^d$?

Given the specific quotient described in the question, the answer is no. Under this quotient there is a fixed point at the origin and the neighborhood of this point quotients to a cone over $RP^{d-1}$....
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Accepted

### Maps to the universal punctured elliptic curve

It is indeed true that a holomorphic map $\mathbb C \to \mathcal E'$ is constant. This is because it must factor through the universal cover of $\mathcal E'$, since $\mathbb C$ is simply connected. ...
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