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Euler class

In mathematics, specifically in algebraic topology, the Euler class is a characteristic class of oriented, real vector bundles. Like other characteristic classes, it measures how "twisted" the vector bundle is. In the case of the tangent bundle of a smooth manifold, it generalizes the classical notion of Euler characteristic. It is named after Leonhard…

Properties, Relations to other invariants & Examples

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Overview

Formal definition

Properties

Relations to other invariants

Examples

Other classes

Sources

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Map overview Semantic statistics

Euler class

Nodes58
Edges57
Triples37
Avg. degree1.97
Density0.034483
Components1

How this topic connects Entity context

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Euler class

Top relations

related to Properties · 8
Euler class → Euler, Functoriality, If, In, Normalization, Orientation, The Euler, Whitney
is a · 6
Euler class → archetype for other characteristic classes of vector bundles, characteristic class of oriented, class whose degree depends on the dimension of the bundle, element of the top cohomology of the manifold, generalization of the Euler characteristic to vector bundles other than tangent bundles, only ordinary cohomology class that detects non-triviality of the tangent bundle of spheres
related to Instability · 6
Euler class → BSO, Euler, In, The, The Euler, Unlike
related to Vanishing locus of generic section · 5
Euler class → Let, Poincaré, Suppose, The Euler, Then
related to Relations to other invariants · 4
Euler class → Euler, In, Thus, Under
related to Squares to top Pontryagin class · 4
Euler class → Chern, Comparing Euler, The, The Pontryagin
related to Formal definition · 2
Euler class → An, The Euler
related to Self-intersection · 2
Euler class → Euler, For

Important terminology Word statistics

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Important terminology

class euler displaystyle bundle characteristic classes tangent vector section oriented rank cohomology manifold real top spheres orientation whitney isbn mathbf

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Euler classis acharacteristic class of oriented0.90text
Euler classis aelement of the top cohomology of the manifold0.90text
Euler classis ageneralization of the Euler characteristic to vector bundles other than tangent bundles0.90text
Euler classis aarchetype for other characteristic classes of vector bundles0.90text
Euler classis aclass whose degree depends on the dimension of the bundle0.90text
Euler classis aonly ordinary cohomology class that detects non-triviality of the tangent bundle of spheres0.90text
Euler classrelated to Formal definitionThe Euler0.60section
Euler classrelated to Formal definitionAn0.60section
Euler classrelated to InstabilityUnlike0.60section
Euler classrelated to InstabilityEuler0.60section
Euler classrelated to InstabilityIn0.60section
Euler classrelated to InstabilityThe Euler0.60section

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