A First Course in String Theory
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2.7 A more general construction for cones?
Consider the plane and the complex coordinate
. We have seen that the identification
, with
an integer greater than two, can be used to construct a cone.
Examine now the identification
where and
are relatively prime integers (their greatest common divisor is one).
…
Determine a fundamental domain for identification.
…
Given two relatively prime numbers a and b, there exists integers m and n such that .
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[guess]
Since M and N are relatively prime numbers, there exists integers m and n such that .
So
.
Therefore,
for some integers m and n.
As a result, a fundamental domain is provided by the points z that satisfy .
[guess]
— Me@2021-03-09 04:58:02 PM
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2021.03.09 Tuesday (c) All rights reserved by ACHK