A First Course in String Theory
2.5 Constructing simple orbifolds
(a) Consider a circle , presented as the real line with the identification . Choose as the fundamental domain. The circle is the space with points identified. The orbifold is defined by imposing the (so-called) identification . Describe the action of this identification on the circle. Show that there are two points on the circle that are left fixed by the action. Find a fundamental domain for the two identifications. Describe the orbifold in simple terms.
Put point and point on the positions that they can form a horizontal diameter.
Then the action is a reflection of the lower semi-circle through the horizontal diameter to the upper semi-circle.
Point and point are the two fixed points.
A possible fundamental domain is .
If a variable point moves from 0 to 1 and then keeps going, that point will actually go back and forth between 0 and 1.
— Me@2020-12-31 04:43:07 PM
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