Singularity Theory
E1046816
Singularity Theory is a branch of mathematics that studies the behavior and classification of functions and spaces near points where they fail to be well-behaved, such as critical points or other types of singularities.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Singularity Theory canonical | 1 |
| cusp catastrophe | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T13561575 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Singularity Theory Context triple: [Vladimir Arnold, notableWork, Singularity Theory]
-
A.
ADE singularity theory
ADE singularity theory is a classification framework in singularity theory and Lie theory that organizes certain simple surface singularities and related algebraic structures into three families labeled A, D, and E.
-
B.
Singular Points of Complex Hypersurfaces
"Singular Points of Complex Hypersurfaces" is a foundational monograph in singularity theory that systematically studies the local and topological properties of singularities arising in complex algebraic and analytic hypersurfaces.
-
C.
Picard–Lefschetz theory
Picard–Lefschetz theory is a branch of algebraic and symplectic geometry that studies how the topology of complex algebraic varieties changes under deformation, particularly via vanishing cycles and monodromy around singularities.
-
D.
Thom–Mather stratification
Thom–Mather stratification is a refined notion of stratification in differential topology that imposes strong regularity and control conditions on how smooth strata fit together, generalizing and strengthening Whitney stratifications.
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E.
Hilbert’s sixteenth problem
Hilbert’s sixteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the topology and arrangement of algebraic curves and surfaces, particularly the number and position of their ovals.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Singularity Theory Target entity description: Singularity Theory is a branch of mathematics that studies the behavior and classification of functions and spaces near points where they fail to be well-behaved, such as critical points or other types of singularities.
-
A.
ADE singularity theory
ADE singularity theory is a classification framework in singularity theory and Lie theory that organizes certain simple surface singularities and related algebraic structures into three families labeled A, D, and E.
-
B.
Singular Points of Complex Hypersurfaces
"Singular Points of Complex Hypersurfaces" is a foundational monograph in singularity theory that systematically studies the local and topological properties of singularities arising in complex algebraic and analytic hypersurfaces.
-
C.
Picard–Lefschetz theory
Picard–Lefschetz theory is a branch of algebraic and symplectic geometry that studies how the topology of complex algebraic varieties changes under deformation, particularly via vanishing cycles and monodromy around singularities.
-
D.
Thom–Mather stratification
Thom–Mather stratification is a refined notion of stratification in differential topology that imposes strong regularity and control conditions on how smooth strata fit together, generalizing and strengthening Whitney stratifications.
-
E.
Hilbert’s sixteenth problem
Hilbert’s sixteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the topology and arrangement of algebraic curves and surfaces, particularly the number and position of their ovals.
- F. None of above. chosen
Statements (72)
| Predicate | Object |
|---|---|
| instanceOf |
branch of mathematics
ⓘ
mathematical theory ⓘ |
| appliesTo |
analytic functions
ⓘ
germs of functions ⓘ holomorphic mappings ⓘ polynomial mappings ⓘ smooth functions ⓘ |
| developedBy |
Hassler Whitney
ⓘ
Heisuke Hironaka ⓘ John Milnor ⓘ Oscar Zariski ⓘ René Thom ⓘ Vladimir Arnold ⓘ |
| fieldOfStudy |
singularities of functions
ⓘ
singularities of spaces ⓘ |
| hasApplicationArea |
control theory
ⓘ
dynamical systems ⓘ mechanics ⓘ optics ⓘ singularities in physical models ⓘ |
| hasKeyResult |
ADE classification of simple singularities
ⓘ
Morse lemma ⓘ Thom’s transversality theorem ⓘ
linked to:
Thom transversality theorem
Whitney stratification ⓘ classification of simple singularities ⓘ resolution of singularities in characteristic zero ⓘ |
| hasSubfield |
equisingularity theory
ⓘ
singularities of algebraic varieties ⓘ singularities of complex hypersurfaces ⓘ singularities of differentiable maps ⓘ topology of singularities ⓘ |
| relatedTo |
algebraic geometry
ⓘ
bifurcation theory ⓘ catastrophe theory ⓘ complex geometry ⓘ differential topology ⓘ topology ⓘ |
| studies |
behavior of functions near singular points
ⓘ
bifurcations of critical points ⓘ catastrophe points ⓘ catastrophes in mappings ⓘ classification of singularities ⓘ critical points of functions ⓘ deformations of singularities ⓘ degenerate critical points ⓘ discriminant sets ⓘ equivalence classes of singularities ⓘ local behavior of algebraic varieties ⓘ local behavior of analytic maps ⓘ local behavior of complex spaces ⓘ local behavior of differentiable maps ⓘ moduli of singularities ⓘ stability of singularities ⓘ |
| usesConcept |
Milnor number
ⓘ
Morse function ⓘ Morse singularity ⓘ bifurcation set ⓘ catastrophe ⓘ critical point ⓘ discriminant locus ⓘ jet space ⓘ non-Morse singularity ⓘ stable mapping ⓘ tangent cone ⓘ unfolding of a singularity ⓘ versal deformation ⓘ |
| usesMethod |
Morse theory
ⓘ
algebraic geometry ⓘ commutative algebra ⓘ complex analytic geometry ⓘ differential topology ⓘ stratification theory ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Singularity Theory Description of subject: Singularity Theory is a branch of mathematics that studies the behavior and classification of functions and spaces near points where they fail to be well-behaved, such as critical points or other types of singularities.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Singularity Theory