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What's the difference between a manifold and an orbifold?

Anonymous Sat 22 Jan 20:47:27 2022 No.14136426 View Reply Original Report

Quoted By: >>14136481 >>14137448

So a manifold is a set, equipped with the standard topology and an atlas that maps to $\mathbb{R}^n$ .

Orbifolds are supposedly generalizations of these, but what's different?

Anonymous

Anonymous Sat 22 Jan 2022 21:02:59 No.14136481 Report

Quoted By: >>14136511

>>14136426
Read the definitions of both. Determine what's missing from one of the definitions but is present in the other.

Anonymous

Anonymous Sat 22 Jan 2022 21:09:57 No.14136511 Report

Quoted By:

>>14136481
I tried. I've just learned about manifolds. I was hoping for a more informal definition for orbifolds.

Anonymous

Anonymous Sat 22 Jan 2022 21:10:00 No.14136512 Report

Quoted By: >>14136526

The definition will make more sense to you if you take or self-teach a DG course. All these diagrams usually look like nonsense until you take the class.

Anonymous

Anonymous Sat 22 Jan 2022 21:12:31 No.14136526 Report

Quoted By:

>>14136512
No, I understand the mapping diagrams. But I want someone to explain orbifolds to me like I'm retarded.

Anonymous

Anonymous Sun 23 Jan 2022 02:37:34 No.14137448 Report

Quoted By:

>>14136426
Orbifolds do not need to be simply connected for one example.

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