fiber bundle Synonyms
No Synonyms and anytonyms found
fiber bundle Meaning
fiber bundle (n)
a bundle of fibers (especially nerve fibers)
fiber bundle Sentence Examples
- In mathematics, a fiber bundle is a structure that consists of a collection of fibers, each of which is a topological space, and a projection map that maps each fiber to a base space.
- Fiber bundles are used to study a wide variety of topological and geometric problems, including classification of manifolds, gauge theory, and knot theory.
- A fiber bundle can be thought of as a generalization of the notion of a covering space, in which the fibers are all homeomorphic to each other.
- In a fiber bundle, the fibers can have different dimensions, and the base space can also have different dimensions.
- Some common examples of fiber bundles include the tangent bundle of a manifold, the normal bundle of a submanifold, and the bundle of linear frames over a manifold.
- Fiber bundles can be classified according to their structure group, which is the group of homeomorphisms of the fibers that preserve the projection map.
- Some important classes of fiber bundles include principal bundles, vector bundles, and associated bundles.
- Fiber bundles are also used in physics to describe the behavior of fields, such as the electromagnetic field and the gravitational field.
- In particular, fiber bundles are used in gauge theory to describe the forces that act between elementary particles.
- Fiber bundles are a powerful tool for studying a wide variety of mathematical and physical problems, and they continue to be an active area of research.
FAQs About the word fiber bundle
a bundle of fibers (especially nerve fibers)
No synonyms found.
No antonyms found.
In mathematics, a fiber bundle is a structure that consists of a collection of fibers, each of which is a topological space, and a projection map that maps each fiber to a base space.
Fiber bundles are used to study a wide variety of topological and geometric problems, including classification of manifolds, gauge theory, and knot theory.
A fiber bundle can be thought of as a generalization of the notion of a covering space, in which the fibers are all homeomorphic to each other.
In a fiber bundle, the fibers can have different dimensions, and the base space can also have different dimensions.
