Thom cobordism theory
E627198
Thom cobordism theory is a foundational branch of algebraic topology developed by René Thom that classifies manifolds up to cobordism using homotopy-theoretic and characteristic class methods.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Thom cobordism theory canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6901170 — 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 cobordism theory Context triple: [René Thom, knownFor, Thom cobordism theory]
-
A.
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.
-
B.
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.
-
C.
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.
-
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.
Milnor K-theory
Milnor K-theory is an algebraic K-theory constructed from fields using tensor powers of their multiplicative groups modulo Steinberg relations, playing a central role in modern algebraic geometry and number theory.
- 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 cobordism theory Target entity description: Thom cobordism theory is a foundational branch of algebraic topology developed by René Thom that classifies manifolds up to cobordism using homotopy-theoretic and characteristic class methods.
-
A.
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.
-
B.
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.
-
C.
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.
-
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.
Milnor K-theory
Milnor K-theory is an algebraic K-theory constructed from fields using tensor powers of their multiplicative groups modulo Steinberg relations, playing a central role in modern algebraic geometry and number theory.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
branch of algebraic topology
ⓘ
cobordism theory ⓘ homotopy-theoretic classification theory ⓘ |
| appliesTo |
smooth manifolds
ⓘ
topological manifolds ⓘ |
| associatedWith |
complex Thom spectrum MU
ⓘ
oriented Thom spectrum MSO ⓘ symplectic Thom spectrum MSp NERFINISHED ⓘ unoriented Thom spectrum MO NERFINISHED ⓘ |
| centralConcept |
bordism group
ⓘ
cobordism ring ⓘ normal bundle ⓘ stable normal bundle ⓘ |
| characterizedBy | Pontryagin–Thom construction NERFINISHED ⓘ |
| classifies |
oriented manifolds up to cobordism
ⓘ
smooth manifolds up to cobordism ⓘ unoriented manifolds up to cobordism ⓘ |
| defines |
complex cobordism ring
ⓘ
oriented cobordism ring ⓘ unoriented cobordism ring ⓘ |
| developedBy | René Thom NERFINISHED ⓘ |
| field | algebraic topology ⓘ |
| goal | classification of manifolds up to cobordism equivalence ⓘ |
| historicalResult |
computation of unoriented cobordism ring
ⓘ
description of oriented cobordism in terms of characteristic numbers ⓘ |
| implies | structure of graded ring on cobordism groups ⓘ |
| influenced |
generalized cohomology theories
ⓘ
stable homotopy theory ⓘ |
| introduces |
Thom space
NERFINISHED
ⓘ
Thom spectrum NERFINISHED ⓘ |
| provides | homotopy-theoretic description of cobordism groups ⓘ |
| relatedTo |
bordism
ⓘ
complex cobordism theory ⓘ generalized homology theories ⓘ surgery theory ⓘ |
| relates |
bordism to characteristic classes
ⓘ
bordism to stable homotopy theory ⓘ cobordism groups to homotopy groups of Thom spectra ⓘ |
| studies | cobordism classes of manifolds ⓘ |
| uses |
Chern classes
NERFINISHED
ⓘ
Euler class NERFINISHED ⓘ Pontryagin classes NERFINISHED ⓘ Pontryagin–Thom collapse map NERFINISHED ⓘ Stiefel–Whitney classes NERFINISHED ⓘ Thom spaces NERFINISHED ⓘ Thom spectra NERFINISHED ⓘ characteristic classes ⓘ homotopy 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: Thom cobordism theory Description of subject: Thom cobordism theory is a foundational branch of algebraic topology developed by René Thom that classifies manifolds up to cobordism using homotopy-theoretic and characteristic class methods.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.