Is orbifolding of the torus a sophisticated spherification?

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In summary, the conversation revolves around the similarities between orbifolds with conical singularities and typical manifolds of Kaluza Klein. The speaker asked for help in understanding how to obtain spheres and CPn spaces from n-dimensional torus, and received answers that seemed to view it as a normal, albeit difficult, process. The mention of the underlying manifold of an orbifold is not common in physics. Additionally, string theoretists refer to the S2 sphere as a "pillow", as seen in a random quote mentioned by the speaker. The conversation continues to be open and the topic remains unresolved.
  • #1
arivero
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I was thinking... perhaps are all these orbifolds with conical singularities simply ironed versions of the typical manifolds of Kaluza Klein? I asked in math overflow about how to get spheres and CPn spaces from n-dimensional torus and the people who answered seem to look at it as usual business, even if difficult to prove in general cases. On other hand the underlying manifold of an orbifold is not mentioned very frequently in physics.

EDIT: It seems that string theoretists like to call to the S2 sphere a "pillow", as in this random quote: "Pictorially, the T 4/Z2 orbifold is a pillow with a torus over it everywhere except at the corners, where the fiber is a pillow"
 
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Thanks for the bump. Actually the MO thread got some answers but the topic seems open.
 

1. What is orbifolding and how does it relate to the torus?

Orbifolding is a mathematical technique used to create new geometric objects by identifying and gluing together points on a given space. The torus is a doughnut-shaped surface and can be orbifolded to create more complex shapes.

2. How is spherification related to orbifolding of the torus?

Spherification is a culinary technique that involves turning liquids into edible spheres. It is related to orbifolding of the torus because the process of orbifolding can create spherical shapes, which can then be used in spherification.

3. Is orbifolding of the torus a difficult process?

Orbifolding of the torus can be a complex and challenging process, as it involves advanced mathematical concepts such as topology and geometry. It requires a deep understanding of these concepts and their applications.

4. What are some real-world applications of orbifolding of the torus?

Orbifolding of the torus has several real-world applications, such as in string theory, where it is used to describe the behavior of particles in multiple dimensions. It is also used in computer graphics to create complex shapes and surfaces.

5. Are there any limitations to orbifolding of the torus?

While orbifolding of the torus is a powerful tool, it does have some limitations. For example, not all shapes can be created through orbifolding, and the process can become increasingly complex for higher-dimensional spaces.

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