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I've seen that the chart mapping diagram commutes for different quotient mapping in some textbooks. Thus I am wondering whether one orbifold ($O$) derived from a (normal) subgroup ($S \lhd G$) can be regarded as its covering orbifold, namely the other orbifold derived from super-group $G$ ($O'=M/G$) would be the quotient orbifolds of $O$.

Is this statement correct? If so, is it the property in commutative diagram vital in this statement? Does the subgroup need to be a normal subgroup?

Erus Izumi
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Gokouu
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1 Answers1

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I am not an expert in orbifolds, while you can still check some previous articles and answers as inspiration. Some concept in "regular" covering map will also help, since deck transformation from another normal subgroup $H \lhd G$ will induce another regular covering.

[1]Choi, S. (2012). Manifolds and $\mathcal {G} $-structures. In Geometric Structures on 2-Orbifolds: Exploration of Discrete Symmetry . Mathematical Society of Japan.

Gokouu
  • 39
Erus Izumi
  • 119