# Simple orbifolds

1. Feb 27, 2013

### rbwang1225

1. The problem statement, all variables and given/known data
This problem comes from the string theory book of Zwiebach, prob. 2.5.
I am constructing the orbifolds $S^1/\mathbb Z_2$ and $T^2/\mathbb Z_2$.

2. Relevant equations
$S^1$ comes from the identification $x\sim x+2$ and choosing the fundamental domain as $-1<x\leq 1$.
$T^2$ are made by $x\sim x+2$ and $y\sim y+2$ and choosing the fundamental domains as $-1<x, y\leq 1$.
$S^1/\mathbb Z_2$ and $T^2/\mathbb Z_2$ are defined by imposing the identification $x\sim-x$ and $(x,y)\sim(-x,-y)$, respectively.

3. The attempt at a solution
By recognizing the identifications, I can know the fixed points of $S^1/\mathbb Z_2$ and $T^2/\mathbb Z_2$.
But my problem is that I can't imagine the resulting pictures of the orbifolds.
Is there any convenient way to figure them out?

Regards.