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Simple orbifolds

  1. Feb 27, 2013 #1
    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.
     
  2. jcsd
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