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Fiber bundle

In mathematics, and particularly topology, a fiber bundle (Commonwealth English: fibre bundle) is a space that is locally a product space, but globally may have a different topological structure. Specifically, the similarity between a space E {\displaystyle E} and a product space B × F {\displaystyle B\times F} is defined using a continuous surjective…

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Overview

History

Formal definition

Examples

Sections

Structure groups and transition functions

Bundle maps

Differentiable fiber bundles

Generalizations

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Map overview Semantic statistics

Fiber bundle

Nodes152
Edges151
Triples83
Avg. degree1.99
Density0.013158
Components1

How this topic connects Entity context

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Fiber bundle

Top relations

related to Structure groups and transition functions · 11
Fiber bundle → Fiber, G-atlas, G-atlases, G-bundle, In, Lie, Specifically, The, This, Two G-atlases, We
related to Differentiable fiber bundles · 10
Fiber bundle → Another, Ehresmann, For, However, If, In, Michor, More, Not, Surjectivity
related to External links · 10
Fiber bundle → Eternity'Sardanashvily, Fibre, Gennadi, Lagrangian, Lectures, Making John Robinson's Symbolic, MathWorld, PlanetMathRowland, Sculpture, Todd
related to Quotient spaces · 10
Fiber bundle → Cartan's, From, G/H, Hopf, If, Lie, One, Steenrod, SU, The
related to Sphere bundles · 9
Fiber bundle → Chern, Euler, For, Given, Gysin, In, Riemannian, TM, When
related to Vector and principal bundles · 6
Fiber bundle → Another, Aut, From, Given, Important, The
related to Bundle maps · 5
Fiber bundle → For, It, Suppose, That, This
related to Generalizations · 5
Fiber bundle → In, Specifically, Steenrod, The, This
related to Trivial bundle · 5
Fiber bundle → Any, CW-complex, Here, Let, Then
is a · 3
Fiber bundle → 4-tuple, continuous map f, fiber bundle in the category of smooth manifolds

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Important terminology

bundle displaystyle fiber space pi map bundles group called projection topology structure one principal base trivial local vector spaces class

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Fiber bundleis a4-tuple0.90text
Fiber bundleis afiber bundle in the category of smooth manifolds0.90text
Fiber bundleis acontinuous map f0.90text
Fiber bundlerelated to Bundle mapsIt0.60section
Fiber bundlerelated to Bundle mapsSuppose0.60section
Fiber bundlerelated to Bundle mapsThat0.60section
Fiber bundlerelated to Bundle mapsFor0.60section
Fiber bundlerelated to Bundle mapsThis0.60section
Fiber bundlerelated to Covering mapIt0.60section
Fiber bundlerelated to Differentiable fiber bundlesIn0.60section
Fiber bundlerelated to Differentiable fiber bundlesNot0.60section
Fiber bundlerelated to Differentiable fiber bundlesFor0.60section

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