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Orbifold matlab problem

  1. Mar 1, 2013 #1
    ##\mathbb Z_{\frac{m}n}## orbifold

    1. The problem statement, all variables and given/known data
    Consider the identification ##z\sim ze^{2\pi i \frac{m}n}##, where ##m## and ##n## are relatively prime integers. Determine a fundamental domain for the identification.

    2. Relevant equations
    Given two relatively prime integers ##a## and ##b##, there exist integers ##m## and ##n## s.t. ##ma+nb=1##.

    3. The attempt at a solution
    By considering cases of small ##m,n##'s, I conclude that the fundamental domain is ##0\le arg(z)<gcd(\frac{2m}n,2)##, but I can't give a more rigorous proof.
    I guess that needs some knowledge of basic number theory.
    Any advices would be very appreciated.

    Regards.
     
  2. jcsd
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