fiber bundle Sentence Examples

  1. 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.
  2. Fiber bundles are used to study a wide variety of topological and geometric problems, including classification of manifolds, gauge theory, and knot theory.
  3. 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.
  4. In a fiber bundle, the fibers can have different dimensions, and the base space can also have different dimensions.
  5. 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.
  6. Fiber bundles can be classified according to their structure group, which is the group of homeomorphisms of the fibers that preserve the projection map.
  7. Some important classes of fiber bundles include principal bundles, vector bundles, and associated bundles.
  8. Fiber bundles are also used in physics to describe the behavior of fields, such as the electromagnetic field and the gravitational field.
  9. In particular, fiber bundles are used in gauge theory to describe the forces that act between elementary particles.
  10. 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.

fiber bundle Meaning

Wordnet

fiber bundle (n)

a bundle of fibers (especially nerve fibers)

Synonyms & Antonyms of fiber bundle

No Synonyms and anytonyms found

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.