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

  • Thread starter "pi"mp
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  • #1
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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!
 

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  • #2
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I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?
 

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