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Line bundle

In mathematics, a line bundle expresses the concept of a line that varies from point to point of a space. For example, a curve in the plane having a tangent line at each point determines a varying line: the tangent bundle is a way of organising these. More formally, in algebraic topology and differential topology, a line bundle is defined as a vector…

Characters, Characteristic classes, universal bundles and classifying spaces & Overview

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Characteristic classes, universal bundles and classifying spaces

Stiefel–Whitney classChern classSmooth structuresExponential sequenceSheaves
17 related topics

Overview

MathematicsLineCurveTangentTangent bundle
26 related topics

Determinant bundles

Exterior powerCotangent bundleSmooth manifoldTensor densitiesOrientable manifold
8 related topics

The tautological bundle on projective space

Projective spaceProjectivizationSerre twisting sheafHomogeneous coordinatesUniversal property
7 related topics

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Overview

The tautological bundle on projective space

Determinant bundles

Characteristic classes, universal bundles and classifying spaces

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Map overview Semantic statistics

Line bundle

Nodes63
Edges62
Triples44
Avg. degree1.97
Density0.031746
Components1

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Line bundle

Top relations

related to Characteristic classes, universal bundles and classifying spaces · 13
Line bundle → According, Analogously, BG, Chern, However, In, One, Stiefel, The, The Chern, There, Those, Whitney
related to Maps to projective space · 10
Line bundle → But, Choosing, Global, However, In, More, Suppose, That, Therefore, This
related to References · 8
Line bundle → Algebraic, AMS Bookstore, ISBN, Line Bundles Archived, Michael Murray, PDF, Robin Hartshorne, Wayback Machine
related to The tautological bundle on projective space · 6
Line bundle → But, Each, One, Serre, The, This
related to Determinant bundles · 4
Line bundle → In, Noetherian, The, This
is a · 2
Line bundle → determinant bundle of the tangent bundle, product of U
see also · 1
Line bundle → I-bundleAmple

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Important terminology

line bundle displaystyle space real bundles point complex vector projective mathbf sections theory algebraic tautological universal classifying map way spaces

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Line bundleis adeterminant bundle of the tangent bundle0.90text
Line bundleis aproduct of U0.90text
Line bundlerelated to Characteristic classes, universal bundles and classifying spacesThe0.60section
Line bundlerelated to Characteristic classes, universal bundles and classifying spacesStiefel0.60section
Line bundlerelated to Characteristic classes, universal bundles and classifying spacesWhitney0.60section
Line bundlerelated to Characteristic classes, universal bundles and classifying spacesAnalogously0.60section
Line bundlerelated to Characteristic classes, universal bundles and classifying spacesChern0.60section
Line bundlerelated to Characteristic classes, universal bundles and classifying spacesHowever0.60section
Line bundlerelated to Characteristic classes, universal bundles and classifying spacesThe Chern0.60section
Line bundlerelated to Characteristic classes, universal bundles and classifying spacesOne0.60section
Line bundlerelated to Characteristic classes, universal bundles and classifying spacesThere0.60section
Line bundlerelated to Characteristic classes, universal bundles and classifying spacesAccording0.60section

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