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Cotangent bundle

In mathematics, especially differential geometry, the cotangent bundle of a smooth manifold is the vector bundle of all the cotangent spaces at every point in the manifold. It may be described also as the dual bundle to the tangent bundle. This may be generalized to categories with more structure than smooth manifolds, such as complex manifolds, or (in…

The cotangent bundle as phase space, Formal definition via diagonal morphism & Examples

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Formal definition via diagonal morphism

Contravariance properties

Examples

The cotangent bundle as phase space

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Cotangent bundle

Nodes50
Edges49
Triples31
Avg. degree1.96
Density0.04
Components1

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Cotangent bundle

Top relations

related to The tautological one-form · 8
Cotangent bundle → Einstein, In, Liouville, Poincaré, So, Suppose, The, This
related to Formal definition via diagonal morphism · 7
Cotangent bundle → Cartesian, Delta, Let, One, The, Then, There
related to The cotangent bundle as phase space · 6
Cotangent bundle → Because, For, Hamiltonian, Since, The, TX
related to Phase space · 5
Cotangent bundle → For, Hamiltonian, If, See Hamiltonian, The
related to Symplectic form · 3
Cotangent bundle → But, Proving, The
related to Examples · 2
Cotangent bundle → Given, The

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Important terminology

displaystyle bundle cotangent smooth one-form symplectic manifold form vector tangent sheaf canonical coordinates point diagonal tautological theta space pullback times

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Cotangent bundlerelated to ExamplesThe0.60section
Cotangent bundlerelated to ExamplesGiven0.60section
Cotangent bundlerelated to Formal definition via diagonal morphismThere0.60section
Cotangent bundlerelated to Formal definition via diagonal morphismOne0.60section
Cotangent bundlerelated to Formal definition via diagonal morphismDelta0.60section
Cotangent bundlerelated to Formal definition via diagonal morphismLet0.60section
Cotangent bundlerelated to Formal definition via diagonal morphismCartesian0.60section
Cotangent bundlerelated to Formal definition via diagonal morphismThe0.60section
Cotangent bundlerelated to Formal definition via diagonal morphismThen0.60section
Cotangent bundlerelated to Phase spaceIf0.60section
Cotangent bundlerelated to Phase spaceFor0.60section
Cotangent bundlerelated to Phase spaceThe0.60section

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