— Me@2021-01-30 05:00:21 PM
2021.01.30 Saturday (c) All rights reserved by ACHK
A First Course in String Theory
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.
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
— Wikipedia on Surface (topology)
The formula for this topology is , which is a sphere.
— Me@2021-01-29 06:10:46 PM
2021.01.29 Friday (c) All rights reserved by ACHK