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meteor
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I would appreciate an explanation about what's an orbibundle
Originally posted by Haelfix
: (I haven't bothered to figure out how to use math yet on these forums)
Originally posted by rick1138
A quick, intuitive description of an orbifold is that an orbifold is a manifold containing isolated singularities that are isomorphic to a cone.
An Orbibundle, also known as an orbifold bundle, is a mathematical object that combines the properties of an orbifold and a fiber bundle. It is a generalization of a principal bundle, where the fibers are replaced by orbifolds.
An orbifold is a geometric object that is a generalization of a manifold. It allows for certain singularities or "folds" in the surface, while still being locally similar to a Euclidean space. It can be thought of as a space that is "folded" in a regular, repeating pattern.
A fiber bundle is a mathematical object that describes the local structure of a space. It consists of a base space and a family of spaces, called fibers, that are attached to each point in the base space. The fibers are all isomorphic to each other, and together they form a continuous space.
An Orbibundle differs from a principal bundle in that the fibers are replaced by orbifolds, which allow for singularities in the structure. The base space of an Orbibundle may also be an orbifold, while a principal bundle has a smooth manifold as its base space.
Orbibundles have applications in various fields of mathematics and physics, including differential geometry, topology, and theoretical physics. They are particularly useful in the study of moduli spaces, which are spaces that represent the different ways in which a geometric object can be deformed or transformed.