Thom–Mather stratification
E285993
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.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Thom–Mather stratification canonical | 1 |
| Thom–Mather stratified structure | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2652997 — 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: Thom–Mather stratification Context triple: [Whitney stratification, relatedConcept, Thom–Mather stratification]
-
A.
Whitney stratification
Whitney stratification is a method in differential topology for decomposing singular spaces into smoothly compatible manifolds (strata) that fit together under specific regularity conditions, enabling rigorous analysis of singularities.
-
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.
Milnor fibration
Milnor fibration is a fundamental construction in singularity theory and differential topology that describes how the complement of a complex hypersurface singularity fibers over the circle, revealing the local topological structure of the singularity.
-
D.
Atiyah–Bott fixed-point theorem
The Atiyah–Bott fixed-point theorem is a fundamental result in equivariant cohomology that expresses global invariants, such as indices of elliptic operators, in terms of local data at the fixed points of a group action.
-
E.
Topology from the Differentiable Viewpoint
"Topology from the Differentiable Viewpoint" is a classic introductory monograph on differential topology that presents key concepts such as smooth manifolds, vector bundles, and characteristic classes in a concise and accessible style.
- 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: Thom–Mather stratification Target entity description: 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.
-
A.
Whitney stratification
Whitney stratification is a method in differential topology for decomposing singular spaces into smoothly compatible manifolds (strata) that fit together under specific regularity conditions, enabling rigorous analysis of singularities.
-
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.
Milnor fibration
Milnor fibration is a fundamental construction in singularity theory and differential topology that describes how the complement of a complex hypersurface singularity fibers over the circle, revealing the local topological structure of the singularity.
-
D.
Atiyah–Bott fixed-point theorem
The Atiyah–Bott fixed-point theorem is a fundamental result in equivariant cohomology that expresses global invariants, such as indices of elliptic operators, in terms of local data at the fixed points of a group action.
-
E.
Topology from the Differentiable Viewpoint
"Topology from the Differentiable Viewpoint" is a classic introductory monograph on differential topology that presents key concepts such as smooth manifolds, vector bundles, and characteristic classes in a concise and accessible style.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
concept in differential topology
ⓘ
geometric structure ⓘ stratification ⓘ |
| aimsTo | control how smooth strata fit together in a singular space ⓘ |
| appliesTo |
smooth manifolds
ⓘ
spaces with singularities ⓘ subanalytic sets ⓘ |
| context |
theory of singular spaces
ⓘ
theory of stratified sets ⓘ |
| ensures |
controlled behavior of singularities
ⓘ
good behavior of maps respecting the stratification ⓘ |
| field |
differential topology
ⓘ
geometric topology ⓘ singularity theory ⓘ |
| generalizes | Whitney stratification ⓘ |
| hasAlternativeName |
Thom–Mather stratification
ⓘ
surface form:
Thom–Mather stratified structure
|
| hasPart | smooth strata ⓘ |
| hasProperty |
compatibility of tubular neighborhoods with stratification
ⓘ
control data on neighborhoods of strata ⓘ frontier condition ⓘ locally finite decomposition into smooth strata ⓘ smooth local triviality along strata in many settings ⓘ topological local triviality along strata ⓘ tubular neighborhood structures around strata ⓘ |
| imposes |
control conditions on how strata fit together
ⓘ
strong regularity conditions ⓘ |
| influenced |
development of stratified Morse theory
ⓘ
subsequent notions of stratified spaces in topology ⓘ |
| isStrongerThan | Whitney stratification ⓘ |
| namedAfter |
John N. Mather
ⓘ
René Thom ⓘ |
| refines | Whitney stratification ⓘ |
| relatedTo |
Whitney stratification
ⓘ
surface form:
Whitney conditions A and B
control data of Mather ⓘ stratified mappings ⓘ stratified vector fields ⓘ topologically stable mappings ⓘ |
| requires |
compatibility of control data with strata
ⓘ
existence of distance functions to strata ⓘ existence of retractions to strata ⓘ |
| usedFor |
analysis of singularities of mappings
ⓘ
construction of stratified Morse theory ⓘ control of isotopies in stratified spaces ⓘ definition of intersection homology on singular spaces ⓘ stratified transversality arguments ⓘ study of stratified spaces ⓘ |
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: Thom–Mather stratification Description of subject: 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.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Thom–Mather stratified structure