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Singularity theory

In mathematics, singularity theory studies spaces that are almost manifolds, but not quite. A string can serve as an example of a one-dimensional manifold, if one neglects its thickness. A singularity can be made by balling it up, dropping it on the floor, and flattening it. In some places the flat string will cross itself in an approximate "X" shape.…

Singularities in algebraic geometry, The smooth theory and catastrophes & Other possible meanings

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Singularities in algebraic geometry

Algebraic curvesCuspIsaac NewtonCubic curvesBézout's theorem
22 related topics

The smooth theory and catastrophes

Catastrophe theoryRené ThomHassler WhitneyCritical pointsSmooth function
20 related topics

Other possible meanings

Mathematical singularityIsolated singularityEssential singularityRemovable singularityMonodromy
7 related topics

How singularities may arise

ProjectionEyesCausticsDegenerationSymmetry
6 related topics

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How singularities may arise

Singularities in algebraic geometry

The smooth theory and catastrophes

Other possible meanings

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Singularity theory

Nodes72
Edges71
Triples30
Avg. degree1.97
Density0.027778
Components1

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Singularity theory

Top relations

related to Arnold's view · 12
Singularity theory → Applications, Arnold, Christopher Zeeman, He, Lie, Taylor, Technically, The, Thom, Vladimir Arnold, While Thom, Whitney
related to The smooth theory and catastrophes · 10
Singularity theory → At, Hassler Whitney, Hironaka's, One, René Thom, Roughly, This, Thom, To, Whitney
related to How singularities may arise · 5
Singularity theory → In, Other, Projection, Singularities, The
related to Other possible meanings · 3
Singularity theory → For, Roughly, The

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Important terminology

singularity singularities theory string point geometry singular points algebraic general one double terms manifold parameters work example stable kind small

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Singularity theoryrelated to Arnold's viewWhile Thom0.60section
Singularity theoryrelated to Arnold's viewChristopher Zeeman0.60section
Singularity theoryrelated to Arnold's viewVladimir Arnold0.60section
Singularity theoryrelated to Arnold's viewHe0.60section
Singularity theoryrelated to Arnold's viewWhitney0.60section
Singularity theoryrelated to Arnold's viewThom0.60section
Singularity theoryrelated to Arnold's viewThe0.60section
Singularity theoryrelated to Arnold's viewTechnically0.60section
Singularity theoryrelated to Arnold's viewLie0.60section
Singularity theoryrelated to Arnold's viewTaylor0.60section
Singularity theoryrelated to Arnold's viewApplications0.60section
Singularity theoryrelated to Arnold's viewArnold0.60section

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