Questions on Orbifolds S^1/Z_2 and T^2/Z_2

1. Apr 5, 2014

"pi"mp

Hi all, I have a few questions on the two spaces S^1/Z_2 and T^2/Z_2. Am I correct in saying that the first space S^1/Z_2 is simply [0,1] where we interpret Z_2 as being the usual action x~-x? Likewise, I know T^2/Z_2 is simply the two-sphere but I can't quite imagine how this is constructed geometrically. Any hints?

Finally, I have a good grasp on quotient spaces from abstract algebra. However, I'm confused by these orbifolds seeming to tell us to "mod out by Z_2" when Z_2 isn't a subgroup of S^1 or T^2. I think it has something to do with group actions but can someone please elaborate on this for me?

Much appreciated!

2. May 4, 2014