Thom space construction
E627199
The Thom space construction is a fundamental operation in algebraic topology that associates a topological space to a vector bundle, playing a central role in cobordism theory and characteristic classes.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Pontryagin–Thom construction | 1 |
| Thom isomorphism | 1 |
| Thom space construction canonical | 1 |
| Thom spaces | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6901171 — 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 space construction Context triple: [René Thom, knownFor, Thom space construction]
-
A.
Whitney approximation theorem
The Whitney approximation theorem is a fundamental result in differential topology stating that any continuous function between smooth manifolds can be uniformly approximated by smooth functions.
-
B.
h-cobordism theorem
The h-cobordism theorem is a fundamental result in differential topology that classifies when two high-dimensional manifolds are diffeomorphic by analyzing the structure of a cobordism between them.
-
C.
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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D.
Atiyah–Hirzebruch spectral sequence
The Atiyah–Hirzebruch spectral sequence is a fundamental computational tool in algebraic topology that relates generalized cohomology theories, such as K-theory, to ordinary cohomology, enabling the step-by-step calculation of these invariants from simpler data.
-
E.
Hirzebruch signature theorem
The Hirzebruch signature theorem is a fundamental result in differential topology that expresses the signature of a smooth, compact, oriented 4k-dimensional manifold as a polynomial in its Pontryagin classes.
- 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 space construction Target entity description: The Thom space construction is a fundamental operation in algebraic topology that associates a topological space to a vector bundle, playing a central role in cobordism theory and characteristic classes.
-
A.
Whitney approximation theorem
The Whitney approximation theorem is a fundamental result in differential topology stating that any continuous function between smooth manifolds can be uniformly approximated by smooth functions.
-
B.
h-cobordism theorem
The h-cobordism theorem is a fundamental result in differential topology that classifies when two high-dimensional manifolds are diffeomorphic by analyzing the structure of a cobordism between them.
-
C.
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.
-
D.
Atiyah–Hirzebruch spectral sequence
The Atiyah–Hirzebruch spectral sequence is a fundamental computational tool in algebraic topology that relates generalized cohomology theories, such as K-theory, to ordinary cohomology, enabling the step-by-step calculation of these invariants from simpler data.
-
E.
Hirzebruch signature theorem
The Hirzebruch signature theorem is a fundamental result in differential topology that expresses the signature of a smooth, compact, oriented 4k-dimensional manifold as a polynomial in its Pontryagin classes.
- F. None of above. chosen
Statements (50)
| Predicate | Object |
|---|---|
| instanceOf |
concept in algebraic topology
ⓘ
topological construction ⓘ |
| appliesTo |
complex vector bundles
ⓘ
oriented vector bundles ⓘ real vector bundles ⓘ stable vector bundles ⓘ topological vector bundles ⓘ |
| centralRoleIn |
cobordism theory
ⓘ
construction of complex cobordism MU ⓘ construction of oriented cobordism MSO ⓘ construction of spin cobordism MSpin ⓘ construction of unoriented cobordism MO ⓘ |
| definitionUses |
collapse map
ⓘ
disk bundle of a vector bundle ⓘ one-point compactification ⓘ quotient space construction ⓘ sphere bundle of a vector bundle ⓘ |
| field |
algebraic topology
ⓘ
cobordism theory ⓘ differential topology ⓘ homotopy theory ⓘ stable homotopy theory ⓘ |
| hasInput |
base space of a vector bundle
ⓘ
total space of a vector bundle ⓘ vector bundle ⓘ |
| hasOutput |
Thom space
ⓘ
pointed topological space ⓘ |
| namedAfter | René Thom NERFINISHED ⓘ |
| property |
compatible with Whitney sum of bundles
ⓘ
functorial up to homotopy ⓘ stable under suspension ⓘ |
| relatedConcept |
Chern classes
ⓘ
Euler class ⓘ Gysin sequence NERFINISHED ⓘ Pontryagin–Thom construction NERFINISHED ⓘ Stiefel–Whitney classes NERFINISHED ⓘ Thom class ⓘ Thom cobordism theory NERFINISHED ⓘ Thom isomorphism NERFINISHED ⓘ Thom spectrum ⓘ orientation of a vector bundle ⓘ |
| usedFor |
associating a topological space to a vector bundle
ⓘ
constructing orientation classes ⓘ defining Gysin maps ⓘ defining Thom isomorphism in cohomology ⓘ defining Thom spectra ⓘ defining cobordism theories ⓘ defining generalized cohomology theories ⓘ studying characteristic classes ⓘ studying embeddings of manifolds ⓘ |
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 space construction Description of subject: The Thom space construction is a fundamental operation in algebraic topology that associates a topological space to a vector bundle, playing a central role in cobordism theory and characteristic classes.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Pontryagin–Thom construction
this entity surface form:
Thom isomorphism
this entity surface form:
Thom spaces