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spaghetti3451
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Homework Statement
Consider the ##(x,y)## plane and the complex coordinate ##z=x+iy##. The identification ##z \sim z\ exp^{(\frac{2 \pi i}{N})}##, with ##N## an integer greater than 2, can be used to construct a cone.Examine now the identification ##z\sim z\ e^{2 \pi i \frac{M}{N}}, N>M \geq 2,## where ##M## and ##N## are relatively prime integers (that is, the greatest common divisor of M and N is 1). Determine a fundamental domain for the identification.
Homework Equations
The Attempt at a Solution
A fundamental domain for the identification is ##0 \leq arg(z) < 2 \pi \frac{Ma+Nb}{N},## because ##Ma+Nb=1## for two integers ##a## and ##b##.
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