A First Course in String Theory
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2.5 Constructing simple orbifolds
(b) Consider a torus , presented as the
plane with the identifications
and
. Choose
as the fundamental domain. The orbifold
is defined by imposing the
identification
.
Prove that there are four points on the torus that are left fixed by the transformation. Show that the orbifold
is topologically a two-dimensional sphere, naturally presented as a square pillowcase with seamed edges.
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To find the fixed points, we consider the cases when and
, where
. Since the length of the interval is only 2, we can consider only the cases when
. Then the only solutions are
— Me@2021-01-17 04:14:44 PM
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— Wikipedia on Surface (topology)
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The formula for this topology is , which is a sphere.
— Me@2021-01-29 06:10:46 PM
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2021.01.29 Friday (c) All rights reserved by ACHK
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