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Principal bundle

In the mathematical area of topology, a principal bundle is a mathematical object that formalizes some of the essential features of the Cartesian product X × G {\displaystyle X\times G} of a topological space X {\displaystyle X} with a group G {\displaystyle G} , but without requiring a product structure. In the same way as with the Cartesian product, a…

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Overview

Formal definition

Examples

Basic properties

Use of the notion

Classification of principal bundles

Sources

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Map overview Semantic statistics

Principal bundle

Nodes92
Edges91
Triples44
Avg. degree1.98
Density0.021739
Components1

How this topic connects Entity context

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Principal bundle

Top relations

related to Other examples · 21
Principal bundle → FM, G/H, GL, Here, Let, Lie, Likewise, Möbius, One, Projective, Recall, Riemannian, Sp, Spin, SU, The, Then, There, These, Variations
related to Characterization of smooth principal bundles · 5
Principal bundle → If, It, Lie, P/G, That
related to Classification of principal bundles · 5
Principal bundle → Any, BG, EG, In, The
is a · 4
Principal bundle → bundle π, frame bundle F, frame bundle of a smooth manifold M, mathematical object that formalizes some of the essential features of the Cartesian product X
related to Trivializations and cross sections · 4
Principal bundle → For, Klein, One, The
related to Associated vector bundles and frames · 3
Principal bundle → GL, If, This
see also · 2
Principal bundle → Associated, G-fibration

Important terminology Word statistics

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Important terminology

displaystyle principal bundle group space structure mathbb bundles action -bundle section product frame identity fibers vector one manifold pi times

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Principal bundleis amathematical object that formalizes some of the essential features of the Cartesian product X0.90text
Principal bundleis abundle π0.90text
Principal bundleis aframe bundle F0.90text
Principal bundleis aframe bundle of a smooth manifold M0.90text
Principal bundlerelated to Associated vector bundles and framesIf0.60section
Principal bundlerelated to Associated vector bundles and framesThis0.60section
Principal bundlerelated to Associated vector bundles and framesGL0.60section
Principal bundlerelated to Characterization of smooth principal bundlesIf0.60section
Principal bundlerelated to Characterization of smooth principal bundlesP/G0.60section
Principal bundlerelated to Characterization of smooth principal bundlesIt0.60section
Principal bundlerelated to Characterization of smooth principal bundlesThat0.60section
Principal bundlerelated to Characterization of smooth principal bundlesLie0.60section

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