A First Course in String Theory
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2.5 Constructing orbifold
(c) Determine the three fixed points of the action on the torus. Show that the orbifold
is topologically a two-dimensional sphere, naturally presented as a triangular pillowcase with seamed edges and corners at the fixed points.
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[guess]
To find the fixed points, we consider the cases when
,
where .
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When ,
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When ,
When ,
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When ,
When ,
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In the fundamental domain, the 3 fixed points are:
when ;
when ;
when .
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Duplicate the fundamental triangle to create a fundamental parallelogram.
If we label the some edges as instead of
, the fundamental parallelogram will have a sphere topology
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However, it is not exactly the same as a sphere topology, because a sphere topology would not have the identification.
[guess]
— Me@2021-02-23 03:44:57 PM
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2021.02.24 Wednesday (c) All rights reserved by ACHK
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