Fiber bundle

In mathematics, in particular in topology, a fiber bundle (or fibre bundle) is a space which locally looks like a product of two spaces but may possess a different global structure. Every fiber bundle consists of a continuous surjective map

Related Topics:
Mathematics - Topology - Product - Continuous - Surjective - Map

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:π : E → B

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where small regions in the total space E look like small regions in the product space

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:B × F.

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Here B is the base space while F is the fiber space. For example, the product space B × F, equipped with π equal to projection onto the first coordinate, is a fiber bundle. This is called the trivial bundle. One goal of the theory of bundles is to quantify, via algebraic invariants, what it means for a bundle to be non-trivial.

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Fiber bundles generalize vector bundles, where the main example is the tangent bundle of a manifold. They play an important role in the fields of differential topology and differential geometry. They are also a fundamental concept in the mathematical formulation of gauge theory.

Related Topics:
Vector bundle - Tangent bundle - Manifold - Differential topology - Differential geometry - Gauge theory

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